On rank two aCM bundles

Let $(F,\cO_F(1))$ 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 $\cE$ of rank $2$ on $F$ such that $h^i\big(F,\cE(t)\big)=0$, for $i=1,\dots,n-1$ and $t\in\bZ$. We obtain some results in the case of a very ample polarization when $n\ge5$. 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 $n\ge4$.