  Let k be an algebraically closed field of characteristic 0. A del Pezzo
threefold F with maximal Picard number is isomorphic to P^1xP^1xP^1, where P^1
is the projective line over k. In the present paper we completely classify
locally free sheaves of rank 2 with vanishing intermediate cohomology over such
an F. Such a classification extends similar results proved by E. Arrondo and L.
Costa regarding del Pezzo threefolds with Picard number 1.
