It is well known that the Horrocks–Mumford bundle [Fscr ] encodes a lot of very interesting geometric information. This is essentially the reason for the fact that much work has been done in order to find other rank-2 bundles on ℙ4. The only nonsplit vector bundles of rank 2 on ℙ4, known up to now, are twists of pullbacks of [Fscr ] by finite coverings f[ratio ]ℙ4→ℙ4. So it seems to be a natural question to consider, instead of ℙ4, other Fano 4-folds. It is the aim of this note to give an example of a rank-2 vector bundle on ℙ1×ℙ3 and to show that it also admits very interesting geometric properties.