  Let X be a nonsingular projective algebraic curve of genus g\ge3. We consider
the moduli space M of stable bundles of fixed determinant with rank n and
degree d coprime and d>n(2g-2). There is a universal bundle on XxM and we
consider the direct image of this bundle on M. With the given restriction on d,
this is a bundle W called the Picard bundle. Our main object in this paper is
to compute the infinitesimal deformations of W. We show also that W possesses a
moduli space and that the connected component of this moduli space containing W
is isomorphic as a polarised variety to the Jacobian of X.
