An adaptive sequential bit synchronizer for a random squarewave data process is proposed in this paper. The probability distributions of the signal parameters and noise process are assumed unknown. The synchronization algorithms, implemented on a small computer, are capable of accurately estimating pulse transition time, pulse amplitude, and pulsewidth simultaneously by invoking the Gauss-Markov theorem. Numerous simulations indicate that the performance of the synchronizer is satisfactory from the points of view of the amount of data required and the speed of convergence.