We construct a family of monads on the Segre variety of type
0 --> O_{P^l\times P^m}(-1,-1)^a --> O_{P^l\times P^m}^b --> O_{P^l\times P^m}(1,1)^c --> 0
and give a cohomological characterisation of torsion free sheaves that are the cohomology of these monads.
