  After a review of several methods designed to produce equivariant cohomology
classes, we apply one introduced by Berline, Getzler and Vergne, to get a
family of representatives of the universal Thom class of a vector bundle.
Surprisingly, this family does not contain the representative given by
Matha\"{\i} and Quillen. However it contains a particularly simple and
symmetric representative that we construct explicitly.
