It is shown that in a dense magnetoactive plasma c/cA ≫ 1 with cold electrons and ions with an anisotropic temperature the ion cyclotron waves propagating along the magnetostatic field are excited with a maximum increment. The dynamics of the quasilinear stage of this instability is investigated. It turns out that, at any moment, the ion distribution function is of the form of a step with the steep front. The speed of the front in the velocity space and the characteristic time of the relaxation process are found. It is ascertained that the distribution function arising in the course of the relaxation is stable with respect to the ion cyclotron waves propagating obliquely to the magnetostatic field.