In rubber friction studies it is usually assumed that the friction force does not depend on the sliding direction, unless the substrate has anisotropic properties, like a steel surface grinded in one direction. Here we will present experimental results for rubber friction, where we observe a strong asymmetry between forward and backward sliding, where forward and backward refer to the run-in direction of the rubber block. The observed effect could be very important in tire applications, where directional properties of the rubber friction could be induced during braking.