We have investigated the digital bit synchronization problem in baseband communication receiver systems using the Gauss-Markov estimation technique which is equivalent to the weighted least square method. The realized bit synchronizer, including the data detector, processes the input signal two dimensionally into the transition phase and data level under the white Gaussian noise environment. We have confrmed the realiation of the bit synchronizer via computer simulation. In addition, we have compared and evaluated the estimation error performance of the proposed method with that of the conventional DTTL method and of the minimum likelihood method.