  Grover's algorithm solves the unstructured search problem. Grover's algorithm
can find the target item with certainty only if searching one out of four.
Grover's algorithm can be deterministic if the phase of the oracle or the
diffusion operator is delicately designed. The precision of the phases could be
a problem. We propose a near-deterministic quantum search algorithm without the
phase control. Our algorithm has the same oracle and diffusion operators as
Grover's algorithm. One additional component is the rescaled diffusion
operator. It acts partially on the database. We show how to improve the success
probability of Grover's algorithm by the partial diffusion operator in two
different ways. The possible cost is one or two more queries to the oracle. We
also design the deterministic search algorithm when searching one out of eight,
sixteen, and thirty-two.
