Reflection symmetry is a kind of important symmetries in geometry, especially it is dominant in the shape of man-made objects. Therefore, retrieving such kind of symmetries in point clouds is of significant interests to engineers. This paper presents a novel algorithm to compute the plane of reflection in point clouds. The point clouds can be noise and incomplete. An intrinsic transformation between the plane of reflection of a model and a coordinate plane is deduced, and the iterated closest points (ICP) algorithm and a solver for systems of nonlinear equations are used to compute the matrix which transforms the normal of the coordinate plane and the origin to the normal of the plane of reflection and a point on the plane. The accuracy of the result is controllable, and this makes the algorithm practical not only for symmetric surface reconstruction in reverse engineering, and geometric completion and beautification as well.