  A four blocks cycle C(k1,k2,k3,k4) is an oriented cycle formed by the union
of four internally disjoint directed paths of lengths k1,k2,k3 and k4
respectively. El Mniny proved that if D is a digraph having a spanning out-tree
T with no subdivisions of C(k, 1, 1, 1), then the chromatic number of D is at
most 8^{3}k. In this paper, we will improve this bound to 18k.
