We propose a complete, d = 6 covariant and kappa-symmetric, action for
the M theory five-brane propagating in D = 11 supergravity background
. This opens a direct way of relating a wide class of super-p-brane so
lutions of string theory with the five-brane of M theory, which should
be useful for studying corresponding dualities and nonperturbative as
pects of these theories.