The equations for the micromaser are derived without assuming the validity of the rotating- wave approximation (RWA) in the Scully-Lamb model for a single-mode maser off resonance. The treatment is based on Swain's continued fractions approach, by which the eigenvalues and eigenvectors of the Hamiltonian describing the system of atoms plus cavity field can be iteratively determined to any desired order and then used to obtain the micromaser equations. These are valid to second order in the parameter g, the coupling constant of the atom-field interaction. The procedure can be extended, to any desired order in g, by successive iterations. Through numerically evaluating the micromaser spectrum we compare our results with those of the RWA. We predict a relative shift, stemming from the Bloch-Siegert shift, which in case of the spectra corresponding to two-photon correlations should be measurable through atomic selective field ionization.