An M-brane and anti-M-brane scheme is proposed to study non-extremal 4
D and 5D black holes, The improved non-extremal intersecting M-brane s
olutions proposed here involve two sets of harmonic functions, The con
straints among the pressures are found, and new features in the M-bran
e and anti-M-brane picture are demonstrated, which resolve the discrep
ancy in the number of free parameters in the D-brane picture. In terms
of the ''numbers'' of M-branes and anti-M-branes, the prefactors of t
he entropies are found to be model independent, and the Bekenstein-Haw
king entropy assumes the duality invariant form which is consistent wi
th the microscopic explanation of the black hole entropy.