The stability of an exact solution of the Navier‐Stokes equations for the flow between two parallel horizontal plates due to a constant reduced pressure gradient in a system rotating about a vertical axis is studied. For zero rotation the stability problem reduces to the classical Orr‐Sommerfeld equation for the stability of plane Poiseuille flow. The variation of the critical Reynolds number with rotation is determined by an expansion procedure for small values of the dimensionless rotation parameter (Taylor number). The effect of small rotation is destabilizing. By using known results for the stability of the Ekman boundary layer an asymptotic result for the critical Reynolds number is obtained for large values of the Taylor number.