This paper describes a local scan matching method that can estimate displacements of position and orientation between two successive scans fast, accurately and robustly. To estimate displacements of position and orientation, the conventional methods need to utilize nonlinear optimization method such as Levenberg-Marquardt method since there is no closed-form solution available which minimizes an evaluation function. Due to such nonlinear optimization method, the conventional method is so time consuming. In this paper, we formulate estimating displacements of position and orientation as a constrained least square problem and provide a closed-form solution which minimizes the evalution function defined by point-to-plane error metric. In the formulation, we show that a quartic function of Lagrange multiplier can be approximated by a linear function. These formulation enables our local scan matching method to be faster than the conventional method. The experimental results in three kinds of real office environment show the usefulness of our method.