This paper presents some initial work done in establishing a complete list of irreducible non-embeddable graphs for the projective plane. The main result presented is the following theorem: All irreducible non-embeddable graphs for the projective plane which have a subgraph contractable to GAMMAsub1 and do not have a subgraph contractable to Ksub3,4, are contractable to one of four graphs listed in the set Ssub2.