diff --git a/src/uu/cp/src/cp.rs b/src/uu/cp/src/cp.rs
index 9664ba66f..4050dd146 100644
--- a/src/uu/cp/src/cp.rs
+++ b/src/uu/cp/src/cp.rs
@@ -918,6 +918,23 @@ fn preserve_hardlinks(
 
             for hard_link in hard_links.iter() {
                 if hard_link.1 == inode {
+                    // Consider the following files:
+                    //
+                    // * `src/f` - a regular file
+                    // * `src/link` - a hard link to `src/f`
+                    // * `dest/src/f` - a different regular file
+                    //
+                    // In this scenario, if we do `cp -a src/ dest/`, it is
+                    // possible that the order of traversal causes `src/link`
+                    // to get copied first (to `dest/src/link`). In that case,
+                    // in order to make sure `dest/src/link` is a hard link to
+                    // `dest/src/f` and `dest/src/f` has the contents of
+                    // `src/f`, we delete the existing file to allow the hard
+                    // linking.
+                    if file_or_link_exists(dest) && file_or_link_exists(Path::new(&hard_link.0)) {
+                        std::fs::remove_file(dest)?;
+                    }
+
                     std::fs::hard_link(hard_link.0.clone(), dest).unwrap();
                     *found_hard_link = true;
                 }
diff --git a/tests/by-util/test_cp.rs b/tests/by-util/test_cp.rs
index 9ced1d130..e1e07878b 100644
--- a/tests/by-util/test_cp.rs
+++ b/tests/by-util/test_cp.rs
@@ -2363,3 +2363,32 @@ fn test_reflink_never_sparse_always() {
     assert_eq!(src_metadata.blocks(), dest_metadata.blocks());
     assert_eq!(dest_metadata.len(), 1024 * 1024);
 }
+
+/// Test for preserving attributes of a hard link in a directory.
+#[test]
+fn test_preserve_hardlink_attributes_in_directory() {
+    let (at, mut ucmd) = at_and_ucmd!();
+
+    // The source directory tree.
+    at.mkdir("src");
+    at.touch("src/f");
+    at.hard_link("src/f", "src/link");
+
+    // The destination directory tree.
+    //
+    // The file `f` already exists, but the `link` does not.
+    at.mkdir_all("dest/src");
+    at.touch("dest/src/f");
+
+    ucmd.args(&["-a", "src", "dest"]).succeeds().no_output();
+
+    // The hard link should now appear in the destination directory tree.
+    //
+    // A hard link should have the same inode as the target file.
+    at.file_exists("dest/src/link");
+    #[cfg(unix)]
+    assert_eq!(
+        at.metadata("dest/src/f").ino(),
+        at.metadata("dest/src/link").ino()
+    );
+}
diff --git a/tests/common/util.rs b/tests/common/util.rs
index 47de18dce..e233d525c 100644
--- a/tests/common/util.rs
+++ b/tests/common/util.rs
@@ -228,6 +228,11 @@ impl CmdResult {
         self
     }
 
+    /// Assert that there is output to neither stderr nor stdout.
+    pub fn no_output(&self) -> &Self {
+        self.no_stdout().no_stderr()
+    }
+
     /// asserts that the command resulted in stdout stream output that equals the
     /// passed in value, trailing whitespace are kept to force strict comparison (#1235)
     /// stdout_only is a better choice unless stderr may or will be non-empty