The nonlinear mechanism for kinetic-Alfvén-wave (KAW) excitation by upper-hybrid waves (UHWs) is discussed. Taking into account perpendicular dispersion of KAWs, caused by effects of finite ion Larmor radius and electron inertia, we examine a new channel for UHW decay, in which a pump UHW decays into another UHW and an ultralow-frequency wave, KAW: UHW→KAW+UHW. A nonlinear dispersion relation is derived, and the growth rate of the parametric decay instability is calculated for a pump UHW propagating at an arbitrary angle to the background magnetic field. We find that the resulting KAWs often have a two-peaked spectrum with different perpendicular dispersions. Using satellite observations, the analytical results are applied to show that the considered process represents an effective mechanism for KAW generation and the consequent spreading of the UHW spectrum in the Earth's magnetosphere and solar corona.