  In the search of YM instanton sheaves with topological charge two, the rank
of beta matrix in the monad construction can be dropped from the bundle case
with rank(beta)= 2 to either rank(beta) = 1 [4] or 0 on some points of CP^3 of
the sheaf cases. In this paper, we first show that the sheaf case with
rank(beta)= 0 does not exist for the previous construction of SU(2) complex YM
instantons [3]. We then show that in the new "extended complex YM instantons"
discovered in this paper, rank(beta) can be either 2 on the whole CP^3 (bundle)
with some given ADHM data or 1, 0 on some points of CP^3 with other ADHM data
(sheaves). These extended SU(2) complex YM instantons have no real instanton
counterparts.
