  This paper examines a way to simplify the circuit of quantum random walk
search algorithm, when the traversing coin is constructed by both generalized
Householder reflection and an additional phase multiplier. If an appropriate
relation between corresponding parameters is realized, our algorithm becomes
more robust to deviations in the phases. In this modification marking coin is
not needed, and all advantages from above mentioned optimization to the
stability, are preserved. It is shown explicitly how to construct such walk
coin in order to obtain more robust quantum algorithm.
