Let chi be a linear morphism of the product of two projective spaces PG(n,F) and PG(m,F) into a projective space. Let gamma be the Segre embedding of such a product. In this paper we give some sufficient conditions for the existence of an automorphism alpha of the product space and a linear morphism of projective spaces psi, such that gammapsi = alphachi. (C) 2002 Elsevier Science B.V. All rights reserved.