On rank two aCM bundles

Let (F,O-F(1)) be a smooth polarized projective variety of dimension n. In the present paper, we prove some easy results on aCM bundles of rank 2 on F, i.e., locally free sheaves epsilon of rank 2 on F such that h(i) (F, epsilon(t)) = 0, for i = 1,...,n-1 and t is an element of Z. We obtain some results in the case of a very ample polarization when n >= 5. We apply these results in order to deal with bundles on non-degenerate complete intersection with degree up to 9. A complete description is given for the complete intersections of two quadrics when n >= 4.