The paper presents a new and original method of m-point estimation of sinusoidal signal amplitude. In this method, an m-point estimator is calculated on the basis of m initial signal samples. The way the estimator is constructed is explained. It is shown that the starting point for constructing the estimator is two initial signal samples. Next, in order to determine the estimator general form, three and m subsequent initial signal samples appearing in a signal period are used. Some special cases of an estimator are considered. Such an estimator is compared with a four-point estimator proposed by Vizireanu and Halunga. It is shown that the m-point estimator makes it possible to estimate the signal amplitude more accurately.