  To any bimodule which is finitely generated and projective on one side one
can associate a coring, known as a comatrix coring. A new description of
comatrix corings in terms of data reminiscent of a Morita context is given. It
is also studied how properties of bimodules are reflected in the associated
comatrix corings. In particular it is shown that separable bimodules give rise
to coseparable comatrix corings, while Frobenius bimodules induce Frobenius
comatrix corings.
