diff --git a/cmd/object-handlers-common.go b/cmd/object-handlers-common.go
index fba7ddbda..9325d8ecf 100644
--- a/cmd/object-handlers-common.go
+++ b/cmd/object-handlers-common.go
@@ -268,6 +268,14 @@ func checkPreconditions(ctx context.Context, w http.ResponseWriter, r *http.Requ
 	ifNoneMatchETagHeader := r.Header.Get(xhttp.IfNoneMatch)
 	if ifNoneMatchETagHeader != "" {
 		if isETagEqual(objInfo.ETag, ifNoneMatchETagHeader) {
+			// Do not care If-Modified-Since, Because:
+			// 1. If If-Modified-Since condition evaluates to true.
+			//  If both of the If-None-Match and If-Modified-Since headers are present in the request as follows:
+			// 	If-None-Match condition evaluates to false , and;
+			//  If-Modified-Since condition evaluates to true ;
+			// 	Then Amazon S3 returns the 304 Not Modified response code.
+			// 2. If If-Modified-Since condition evaluates to false, The following `ifModifiedSinceHeader` judgment will also return 304
+
 			// If the object ETag matches with the specified ETag.
 			writeHeadersPrecondition(w, objInfo)
 			w.WriteHeader(http.StatusNotModified)
@@ -304,7 +312,7 @@ func checkPreconditions(ctx context.Context, w http.ResponseWriter, r *http.Requ
 	// If-Unmodified-Since : Return the object only if it has not been modified since the specified
 	// time, otherwise return a 412 (precondition failed).
 	ifUnmodifiedSinceHeader := r.Header.Get(xhttp.IfUnmodifiedSince)
-	if ifUnmodifiedSinceHeader != "" {
+	if ifUnmodifiedSinceHeader != "" && ifMatchETagHeader == "" {
 		if givenTime, err := amztime.ParseHeader(ifUnmodifiedSinceHeader); err == nil {
 			if ifModifiedSince(objInfo.ModTime, givenTime) {
 				// If the object is modified since the specified time.
diff --git a/cmd/object-handlers-common_test.go b/cmd/object-handlers-common_test.go
index 6d190a95e..08a787f73 100644
--- a/cmd/object-handlers-common_test.go
+++ b/cmd/object-handlers-common_test.go
@@ -18,7 +18,14 @@
 package cmd
 
 import (
+	"bytes"
+	"context"
+	"net/http"
+	"net/http/httptest"
 	"testing"
+	"time"
+
+	xhttp "github.com/minio/minio/internal/http"
 )
 
 // Tests - canonicalizeETag()
@@ -51,3 +58,125 @@ func TestCanonicalizeETag(t *testing.T) {
 		}
 	}
 }
+
+// Tests - CheckPreconditions()
+func TestCheckPreconditions(t *testing.T) {
+	objModTime := time.Date(2024, time.August, 26, 0o2, 0o1, 0o1, 0, time.UTC)
+	objInfo := ObjectInfo{ETag: "aa", ModTime: objModTime}
+	testCases := []struct {
+		name              string
+		ifMatch           string
+		ifNoneMatch       string
+		ifModifiedSince   string
+		ifUnmodifiedSince string
+		objInfo           ObjectInfo
+		expectedFlag      bool
+		expectedCode      int
+	}{
+		// If-None-Match(false) and If-Modified-Since(true)
+		{
+			name:            "If-None-Match1",
+			ifNoneMatch:     "aa",
+			ifModifiedSince: "Sun, 26 Aug 2024 02:01:00 GMT",
+			objInfo:         objInfo,
+			expectedFlag:    true,
+			expectedCode:    304,
+		},
+		// If-Modified-Since(false)
+		{
+			name:            "If-None-Match2",
+			ifNoneMatch:     "aaa",
+			ifModifiedSince: "Sun, 26 Aug 2024 02:01:01 GMT",
+			objInfo:         objInfo,
+			expectedFlag:    true,
+			expectedCode:    304,
+		},
+		{
+			name:            "If-None-Match3",
+			ifNoneMatch:     "aaa",
+			ifModifiedSince: "Sun, 26 Aug 2024 02:01:02 GMT",
+			objInfo:         objInfo,
+			expectedFlag:    true,
+			expectedCode:    304,
+		},
+	}
+	for _, tc := range testCases {
+		t.Run(tc.name, func(t *testing.T) {
+			recorder := httptest.NewRecorder()
+			request := httptest.NewRequest(http.MethodHead, "/bucket/a", bytes.NewReader([]byte{}))
+			request.Header.Set(xhttp.IfNoneMatch, tc.ifNoneMatch)
+			request.Header.Set(xhttp.IfModifiedSince, tc.ifModifiedSince)
+			request.Header.Set(xhttp.IfMatch, tc.ifMatch)
+			request.Header.Set(xhttp.IfUnmodifiedSince, tc.ifUnmodifiedSince)
+			actualFlag := checkPreconditions(context.Background(), recorder, request, tc.objInfo, ObjectOptions{})
+			if tc.expectedFlag != actualFlag {
+				t.Errorf("test: %s, got flag: %v, want: %v", tc.name, actualFlag, tc.expectedFlag)
+			}
+			if tc.expectedCode != recorder.Code {
+				t.Errorf("test: %s, got code: %d, want: %d", tc.name, recorder.Code, tc.expectedCode)
+			}
+		})
+	}
+	testCases = []struct {
+		name              string
+		ifMatch           string
+		ifNoneMatch       string
+		ifModifiedSince   string
+		ifUnmodifiedSince string
+		objInfo           ObjectInfo
+		expectedFlag      bool
+		expectedCode      int
+	}{
+		// If-Match(true) and If-Unmodified-Since(false)
+		{
+			name:              "If-Match1",
+			ifMatch:           "aa",
+			ifUnmodifiedSince: "Sun, 26 Aug 2024 02:01:00 GMT",
+			objInfo:           objInfo,
+			expectedFlag:      false,
+			expectedCode:      200,
+		},
+		// If-Unmodified-Since(true)
+		{
+			name:              "If-Match2",
+			ifMatch:           "aa",
+			ifUnmodifiedSince: "Sun, 26 Aug 2024 02:01:01 GMT",
+			objInfo:           objInfo,
+			expectedFlag:      false,
+			expectedCode:      200,
+		},
+		{
+			name:              "If-Match3",
+			ifMatch:           "aa",
+			ifUnmodifiedSince: "Sun, 26 Aug 2024 02:01:02 GMT",
+			objInfo:           objInfo,
+			expectedFlag:      false,
+			expectedCode:      200,
+		},
+		// If-Match(true)
+		{
+			name:         "If-Match4",
+			ifMatch:      "aa",
+			objInfo:      objInfo,
+			expectedFlag: false,
+			expectedCode: 200,
+		},
+	}
+	for _, tc := range testCases {
+		t.Run(tc.name, func(t *testing.T) {
+			recorder := httptest.NewRecorder()
+			request := httptest.NewRequest(http.MethodHead, "/bucket/a", bytes.NewReader([]byte{}))
+			request.Header.Set(xhttp.IfNoneMatch, tc.ifNoneMatch)
+			request.Header.Set(xhttp.IfModifiedSince, tc.ifModifiedSince)
+			request.Header.Set(xhttp.IfMatch, tc.ifMatch)
+			request.Header.Set(xhttp.IfUnmodifiedSince, tc.ifUnmodifiedSince)
+			actualFlag := checkPreconditions(context.Background(), recorder, request, tc.objInfo, ObjectOptions{})
+			if tc.expectedFlag != actualFlag {
+				t.Errorf("test: %s, got flag: %v, want: %v", tc.name, actualFlag, tc.expectedFlag)
+			}
+			if tc.expectedCode != recorder.Code {
+				t.Errorf("test: %s, got code: %d, want: %d", tc.name, recorder.Code, tc.expectedCode)
+			}
+		})
+	}
+}