The optical ray properties of the cube-corner retroreflector (CCR) are first recalled. The change of polarization of the radiation due to CCR reflection is then derived by use of the Mueller matrix calculus. It is found that, in general, when the faces are not ideal reflectors, the useful cross section of the CCR consists of six zones, each of which produces a different change of polarization, i.e., it gives a different Mueller matrix. All the Mueller matrices depend on wavelength. The results are quite general and can be used directly also for partially polarized radiation.