How do I update an AppImage that is not auto-updateable?

I am trying to update an AppImage and tried the steps provided in How to update appimage. However, when I use the AppImageUpdate tool as described in the post, it gives me the following error:

Error reading AppImage: Could not find update information in the AppImage. Please contact the author of the AppImage and ask them to embed update information.

What is now the best way for me to update the AppImage? An updated version is available for download.