  The specific heat of the two-dimensional $\pm J$ Ising model has been
investigated by the numerical transfer matrix method and Monte Carlo
simulations from a new point of view. The region where a part of the specific
heat takes the negative value has been investigated, which is characteristic of
frustrated systems and reflects the non-trivial degeneracy of the ground state.
The region mentioned above is found to be fairly large in the $p-T$ plane ($p$
is the concentration of the ferromagnetic bond and $T$ is the temperature).
Moreover, it includes the Nishimori line. Namely, it includes a part of the
paramagnetic-ferromagnetic phase boundary, on which the specific heat cannot
diverge. The present result indicates that the specific heat does not diverge
at least on a part of the paramagnetic-ferromagnetic phase boundary above the
multicritical point, which is in conflict with previous results.
