The Mueller matrix M¿ for atmospheric aerosol backscattering in Utah (a desert environment) is derived from lidar-polarized backscattering measurements at CO2 wavelengths for a horizontal path a few meters above the ground. The Mueller matrix is nearly a diagonal matrix, with m11=S11, m=22=(S22-S33)/2, and m33≅-m22, as is expected for randomly oriented aerosols with axial symmetry. The ratio m22/m11 is approximately 0.75, for which the linear depolarization ratio is approximately 0.15. In computing the Mueller matrix from lidar-polarized backscattering measurements of various combinations of transmit/receive polarizations (xy), two steps are employed: (1) a deconvolution process to produce a lidar signal pxy(r) from the polarized lidar measurements by deconvolving the long CO2 laser pulse and the lidar system impulse-response function (i.e., removing their smearing effect from the measured lidar signal), and (2) a constrained slope method to produce an aerosol backscattering coefficient βxy, for each polarization configuration xy, from which the Mueller matrix is computed. ¿ 1998 American Geophysical Union