This paper discusses the estimation method of the satellite attitude when star sensors are the only attitude sensors. Among the previously proposed estimation methods, the algebraic method and the q-method are representative ones. The algebraic method is fast but less accurate, whereas the q-method gives the optimal solution but takes much more time. The proposed method uses the solution of the algebraic method as an initial estimate and applies Newton method to obtain a more accurate solution by iterations. The iteration procedure is simplified by using the estimate of the last iteration. Thus the calculation time is shortened. From numerical simulations, it is shown that the proposed method gives the same optimal solution as the q-method and is much faster than the q-method. The proposed method is fairly competitive in calculation time, compared with the Markley's method (a variation of the q-method) credited as the fastest optimal estimation method. Besides computation of four rules (+, -, × and ÷), Markley's method includes seven square roots computation, a trigonometric function and an inverse trigonometric function, whereas the proposed method includes only two square roots computation. Therefore, in view of on-board applications, the proposed method is more suitable.