The parametric decay of an ion cyclotron pump wave in the high-speed solar wind streams is studied. The pump wave is an exact stationary solution of the Vlasov equation and Maxwell's equations, and it decays parametrically into an ion acoustic and a product ion cyclotron wave. The case where all the waves propagate parametric decay instability. Although this instability has been considered important for the Alfv¿n wave, the calculation shows that it is probably not important for the ion cyclotron wave, since the range of wave number values where the growth rate is above threshold is very small.