Abstract: By performing modulational instability analysis of the the nonlinear coupled dimensionless equations between a fast magnetosonic wave (FMSW) propagating obliquely with the magnetic field and a low-frequency slow Alfvén wave (SAW), we obtain the dispersion relation of the perturbation wave. The growth rate of the perturbation wave is obtained. It is found that the growth rate increases as background magnetic field increases, which is in agreement with that reported by Tiwary et al (2016 Phys. Plasmas 23 122307). A critical perturbation wave number is found. When the perturbation wave number is greater than or equal to the critical value, the growth rate is positive and it increases as the perturbation wave number increases, while the wave is stable. The maximum growth rate is reached when the frequency of the FMSW is half of the ion cyclotron frequency. The minimum growth rate is reached when the propagation direction of the perturbation wave is the same as that of the FMSW.