86 Cavalier starter problem

I just installed a new starter in my car. The starter makes a high pitch whine for about a second after the engine starts. My GM manual says to add full length shims to the starter one at a time until the noise stops and not to use more than four shims. I'm up to four shims and the noise persists. How do I fix this? Your help would be greatly appreciated.

This starter has a bad gear unit. Replace this starter or you could dammage your flywheel.