Genesis 1 and 2 - Contradictory?

As I peruse the bible I discover that Genesis, chap. 1 and 2 appear contradictory, specifically with regards to the order of human and animal creation.Genesis 1 posits that animals were created first by god, and then humans were made ("male and female, He created them") to have dominion over them.But then, in Genesis 2, god makes male man and then creates animals (male and female) to be his companions. Only then is the female created.Doesn't this pose an irreconcilable contradiction to anyone who would seek to use the Genesis story (rather, the two Genesis stories) as a literal account of the creation of life? It's pretty clear to me (trained in literary criticism) that the second account cannot be simply an elaboration of the first. It's simply too contradictiory.------------------
Epimenedes Signature: This is not a signature.

I disagree that a non-chronological interpretation is supported by the text. For instance, my version (KJV) at least uses words like "Then the Lord..." and "So the Lord..." etc. These phrases clearly represent a chronological narrative.Perhaps I'm using the wrong bible. Do biblical creationists have a favored translation?