**Corollary 4.1**: *Any cone, which admits a flock, admits a linear flock. *

*Pf*: If a cone C(V,S) admits a flock, then by Theorem 3.1, the carrier S is not a blocking set in . Thus, there is a line *l* in which does not intersect S, and hence does not intersect C(V,S). The q planes through *l* which do not contain V form a linear flock of C(V,S).