An experimental study of the viscosity of a macroscopic suspension, i.e., a suspension for which Brownian motion can be neglected, under steady shear is presented. The suspension is prepared with a high packing fraction and is density matched in a Newtonian carrier fluid. The viscosity of the suspension depends on the shear rate and the time of shearing. It is shown that a macroscopic suspension shows thixotropic viscosity, i.e., shear thinning with a long relaxation time as a unique function of shear. The relaxation times show a systematic decrease with increasing shear rate. These relaxation times are larger when decreasing the shear rates, compared to those observed after increasing the shear. The time scales involved are about 10 000 times larger than the viscous time scale tau(visc)=a2/nu and about 1000 times smaller than the thermodynamic time scale tau(therm)=Pe/gamma. (a is the gap width of the viscometer, nu is the kinematic viscosity, Pe=6pi(eta)gamma;tau)3/(k(B)T) is the Péclet number and gamma; is the shear rate.) The structure of the suspension at the outer cylinder of a viscometer is monitored with a camera, showing the formation of a hexagonal structure. The temporal decrease of the viscosity under shear coincides with the formation of this hexagonal pattern.