Hi donaghue.

Please follow the instructions in Update Firefox to the latest release help article. Under the common three steps is also information what to do, if the update was not successful.

Hello please download and install firefox, try next steps:

1. Download a copy of the latest firefox from http://www.mozilla.org/en-US/firefox/all.html (full dmg package)

2. Trash the current Firefox application to do a clean install.

3. Install the version that you have downloaded.

Do not select to remove your personal data, your profile data is stored elsewhere in the Firefox Profile Folder, so you won't lose your bookmarks or other personal data.

thank you

If the above does not help,

Download Firefox For All languages And Systems {web link} Save the file. Then;

Using your file browser, open the Programs Folder on your computer.

Windows: C:\Program Files C:\Program Files (x86) Mac: Open the "Applications" folder. Linux: Check your user manual.

Look for, and rename any Mozilla or Firefox folders by adding .old to them.

After rebooting the computer, run the installer. If all goes well, remove the OLD folders when you are done.

FredMcD, you repeated much of what was said already and your reply was best suited for Windows and there is no installer on Mac OSX.

Also you last part can confuse users into accidentally deleting their Profiles even though you think your comments only applies to the Firefox application folder.

Looking for anything Mozilla or Firefox related WILL bring up their Profiles and not just the Firefox application folder if they can view hidden folders/files.

donaghue said

The problem is stated above. The download finishes (repeatedly) and I re-start Firefox (repeatedly) but version 38.0.5 does not change which would be fine, I guess,. except that every time I open Firefox, a message pops up asking me to update. Help would be appreciated. Thank you.

By downloading do you mean updates in Firefox or by saving the Firefox 43.0.4.dmg file from mozilla.org ?

If downloading then you have to actually install it as downloading file alone is not sufficient.

See https://support.mozilla.org/en-US/kb/how-download-and-install-firefox-mac