diff --git a/CHANGELOG.md b/CHANGELOG.md
index aacb7819b24..6ffa4e88747 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -26,6 +26,7 @@ We refer to [GitHub issues](https://github.com/JabRef/jabref/issues) by using `#
 - We fixed an issue where the ampersand character wasn't rendering correctly on previews. [#3840](https://github.com/JabRef/jabref/issues/3840)
 - We fixed an issue where an erroneous "The library has been modified by another program" message was shown when saving. [#4877](https://github.com/JabRef/jabref/issues/4877)
 - We fixed an issue where the file extension was missing after downloading a file (we now fall-back to pdf). [#5816](https://github.com/JabRef/jabref/issues/5816)
+- We fixed an issue where cleaning up entries broke web URLs, if "Make paths of linked files relative (if possible)" was enabled, which resulted in various other issues subsequently. [#5861](https://github.com/JabRef/jabref/issues/5861)
 
 ### Removed
 - Ampersands are no longer escaped by default in the `bib` file. If you want to keep the current behaviour, you can use the new "Escape Ampersands" formatter as a save action.
diff --git a/src/main/java/org/jabref/logic/cleanup/RelativePathsCleanup.java b/src/main/java/org/jabref/logic/cleanup/RelativePathsCleanup.java
index 9b18e939782..1bbecb2f41c 100644
--- a/src/main/java/org/jabref/logic/cleanup/RelativePathsCleanup.java
+++ b/src/main/java/org/jabref/logic/cleanup/RelativePathsCleanup.java
@@ -33,10 +33,17 @@ public List<FieldChange> cleanup(BibEntry entry) {
 
         for (LinkedFile fileEntry : fileList) {
             String oldFileName = fileEntry.getLink();
-            String newFileName = FileUtil
-                    .relativize(Paths.get(oldFileName), databaseContext.getFileDirectoriesAsPaths(filePreferences))
-                    .toString();
-
+            String newFileName = null;
+            if (fileEntry.isOnlineLink()) {
+                // keep online link untouched
+                newFileName = oldFileName;
+            }
+            else {
+                // only try to transform local file path to relative one
+                newFileName = FileUtil
+                        .relativize(Paths.get(oldFileName), databaseContext.getFileDirectoriesAsPaths(filePreferences))
+                        .toString();
+            }
             LinkedFile newFileEntry = fileEntry;
             if (!oldFileName.equals(newFileName)) {
                 newFileEntry = new LinkedFile(fileEntry.getDescription(), newFileName, fileEntry.getFileType());
@@ -56,5 +63,4 @@ public List<FieldChange> cleanup(BibEntry entry) {
 
         return Collections.emptyList();
     }
-
 }
diff --git a/src/main/java/org/jabref/model/entry/LinkedFile.java b/src/main/java/org/jabref/model/entry/LinkedFile.java
index 62a71dac417..3c79ffd6812 100644
--- a/src/main/java/org/jabref/model/entry/LinkedFile.java
+++ b/src/main/java/org/jabref/model/entry/LinkedFile.java
@@ -135,10 +135,11 @@ private void readObject(ObjectInputStream in) throws IOException {
     /**
      * Checks if the given String is an online link
      * @param toCheck The String to check
-     * @return True if it starts with http://, https:// or contains www; false otherwise
+     * @return <code>true</code>, if it starts with "http://", "https://" or contains "www."; <code>false</code> otherwise
      */
     private boolean isOnlineLink(String toCheck) {
-        return toCheck.startsWith("http://") || toCheck.startsWith("https://") || toCheck.contains("www.");
+        String normalizedFilePath = toCheck.trim().toLowerCase();
+        return normalizedFilePath.startsWith("http://") || normalizedFilePath.startsWith("https://") || normalizedFilePath.contains("www.");
     }
 
     @Override