This paper is a continuation of [2], presenting some more results leading to establishing a complete list of irreducible non-embeddable graphs for the projective plane. The main result presented here is the following theorem: all irreducible non-embeddable graphs for the projective plane which have a subgraph contractable to Esub2 and do not have a subgraph contractable to Esub1 or GAMMAsub1 or Ksub3,4 are contractable to one of the 3 graphs Fsub3,Fsub4 or Esub20 in [E].