Cumulant sequences have become a more and more powerful tool in statistical signal processing. Through modulation of cumulant sequences we have inserted some degrees of freedom called modulation frequencies. We will show the usefulness of this modulated cumulant sequences by a new linear method for MA-parameter estimation which avoids some disadvantages of existing methods. Furthermore, we develop a modification of the method for additive arbitrarily distributed noise. Extensive simulations have shown a significant improvement of the parameter estimation accuracy.