Squeaky Corolla

I have a 96 corolla with 239,000 miles on it and just recently it started making a high pitched squeaking or squealing noise when it starts up. I had the serpentine belt change thinking that was it and it stopped for a while and now it is doing it again. It is the loudest when I am backing out of the driveway but then stops after I go less than a block. What else should I consider.

I would take it back to whoever changed it.  See what they say.  I would be looking at each pulley on that belt.  I suspect you will find a problem with one of them.