We consider the problem of searching for an unpredictable moving target, using a robot that lacks a map of the environment, lacks the ability to construct a map, and has imperfect navigation ability. We present a complete algorithm, which yields a motion strategy for the robot that guarantees the elusive target will be detected, if such a strategy exists. It is assumed that the robot has an omnidirectional sensing device that is used to detect moving targets and also discontinuities in depth data in a 2D environment. We also show that the robot has the same problem solving power as a robot that has a complete map and perfect navigation abilities. The algorithm has been implemented in simulation, and some examples are shown.