Recently, Markov sources were shown to achieve 100% fault efficiency at low area overhead when used as pseudo-random pattern generators in scan BIST. In this paper we give a new method of designing Markov sources. The new design attempts to match probabilities of 1 to 0 and 0 to 1 transitions in consecutive bits of a set of test vectors, taking into account that the transition probabilities may be different for different bit positions. Experimental results show that the proposed method considerably reduces the hardware overhead and test lengths required to achieve 100% fault coverage.