Conventional linear prediction algorithm with sinusoidal signal for the estimation of motor's speed has a limitation in the range of low speed. If an estimator can get additional information then its performance is able to be improved. A sinusoidal signal has the natural property which is quadratic equation so called Pythagorean identity. However, since the equation was nonlinear form, it needs change to a linear constrained condition. Adding it to the measurement equation, it is possible to derive a linear state space equation which has more information without additional sensor. The experimental results and the computer simulations show that the performance of the proposed algorithm in this study is better than that of the conventional algorithm. It supports that the additional constrained condition can improve the estimator's performance.