Synchronizing clocks is crucial for distributed safety-critical in-vehicle applications. Since Controller Area Network (CAN) is the predominant in-vehicle communication bus, it is highly relevant to realize clock synchronization (CS) on CAN. This paper proposes a new software-based CS (SW-CS) algorithm based on the periodic transmission of reference messages (RMs) by a Master node and discrete-time feedback control. Different from existing algorithms, that only update clocks after receiving a RM, our algorithm corrects the clock drift between RMs. Measurements on a hardware setup show a decrease of the clock differences by more than one order of magnitude.