This contradiction focuses on a fascinating little theological dispute over whether baptisms are to be performed in the name of Jesus (alone) or using the trinitarian formula of Matthew 28:19. Here are all the relevant verses: KJV, NIV
So far, all of the apologetical attempts to deal with this problem seem to hinge on the implicit claim that the author of Acts meant "in the name of" to mean something different than the author of gMatt when he uses the same Greek words. Obviously, this is unwarranted special pleading. Thus far, I've not found any convincing answers to this little conundrum, trivial though it may seem.