A nonlinear process, involving the parametric decay of electrostatic ion cyclotron waves into a shear Alfv¿n wave and an electrostatic sideband, is investigated as a possible internal source mechanism of the low-frequency magnetic pulsations in the magnetosphere. The process is applicable to the pulsations with frequency &ohgr;≲0.03 &ohgr;ci (ion cyclotron frequency) and may cover the periodicity range of Pc 2 and Pc 5. The threshold for the process is set by the gradients in plasma density and magnetic field. In magnetospheric plasma the threshold is exceeded when the energy density of the pump wave fluctuations is of the order of a few percent of thermal energy density.