  When searching for a marked vertex in a graph, Szegedy's usual search
operator is defined by using the transition probability matrix of the random
walk with absorbing barriers at the marked vertices. Instead of using this
operator, we analyze searching with Szegedy's quantum walk by using reflections
around the marked vertices, that is, the standard form of quantum query. We
show we can boost the probability to 1 of finding a marked vertex in the
complete graph. Numerical simulations suggests that the success probability can
be improved for other graphs, like the two-dimensional grid. We also prove
that, for a certain class of graphs, we can express Szegedy's search operator,
obtained from the absorbing walk, using the standard query model.
