We propose an operating condition for an optically pumped scalar atomic magnetometer with a unique band-pass frequency response. Under this operating condition, the signal response of the magnetometer is increased threefold around a nonzero resonance frequency. The resonance frequency is equal to the detuning between the Larmor frequency and the frequency of the oscillating magnetic field used for excitation. The resonance is explained in terms of the characteristics of the first-order perturbation expansion of the Bloch equation for a modulated bias magnetic field. The scalar magnetometer provides an enhanced magnetic response around its resonance frequency even beyond the cutoff frequency, which is defined as the inverse of the phase relaxation time of the spin polarization.