  We reformulate the canonical seesaw mechanism in the case that the
electroweak gauge symmetry is unbroken, and show that it can "formally" work
and allow us to derive an exact seesaw formula for the light and heavy Majorana
neutrinos. We elucidate the reason why there is a mismatch between the mass
eigenstates of heavy Majorana neutrinos associated with thermal leptogenesis
and those associated with the seesaw framework, and establish the exact and
explicit relations between the "original" and "derivational" seesaw parameters
by using an Euler-like parametrization of the $6\times 6$ active-sterile flavor
mixing matrix.
