On the basis of Fisher's method, singularity of specific heat near the transition point is studied for the Ising or Heisenberg model with an arbitrary value of spin and range of interaction. The following results are obtained for a reasonable distribution of zeros of canonical partition function. (a) If the specific heat has a singularity C+(T-Tc)-α above the transition point Tc, it should have a singularity C-(Tc-T)-α below Tc, C- being not necessarily equal to C+. (b) If the specific heat has a logarithmic singularity -Aln(T-Tc)+B+ above Tc, it should have a singularity -Aln(Tc-T)+B- below Tc, B- being not necessarily equal to B+. Some theoretical and experimental works so far reported are discussed in the light of these results.