We calculate the canonical partition function of the ideal Bose-Einstein gas by the modified method of steepest descent without the continuous spectrum approximation in the cases of periodic boundary condition and of perfectly reflecing well condition. Above the critical point the steepest curve is the ordinary one through the saddle point. At and below the lambda temperature the steepest curve is such that the singularity of the integrand lies on it as a cusp, and the ordinary saddle point method loses its validity. The evaluation of the residual term in the integration, however, justifies the usual expression of the extensive quantities per particle and intensive quantities as N and V sufficiently large. In deriving the above results, a sufficient condition for the justification of the substitution of bl0 for bl0(V) in canonical partition function of the imperfect gas is given and discussed.