The apparent wall slip velocity coefficient of concentrated monodisperse suspensions of 90 mu m PMMA particles in a viscous Newtonian fluid was determined experimentally in a narrow gap Couette device by measuring the particle velocities across the gap using a laser doppler anemometer system and then extrapolating the results to the two walls. The slip coefficients thereby obtained were found to be insensitive to the magnitude of the applied shear rate and to equal, approximately, lambda/8 for particle concentrations phi in the range 0.45 less than or equal to phi less than or equal to 0.52, where lambda refers to the relative effective viscosity of the suspension with respect to that of the pure fluid.