We analysed a time series of nine consecutive years of high-precision photometry of the spotted RS CVn star UZ Lib by using a discrete Fourier-transform technique and a non-linear least-squares minimization. The main period of 4.77-days due to stellar rotation was resolved into three individual periods separated by -0.2% and +0.4% around the main period. The stability of the spot pattern over many years, as derived from our contemporaneous Doppler images, allowed us to relate the different periods to co-existing spots at different latitudes, and thus to the direct determination of the strength and the sign of the differential rotation. The main period originates from the equatorial surface regions and is practically the same as the orbital period from independent radial-velocity measurements, suggesting that the stellar equator is tidally locked to the orbital motion. The higher latitudes rotate slightly faster than the equator, suggesting non-solar differential rotation with a parameter of α=ΔΩ/Ω=-0.0026, 80 times weaker than on the solar surface, and a lap time of Pequator/α≃-1800-days, i.e. 14 times longer than for the Sun.