A new identification method is proposed for estimating the parameters of a discrete-time linear dynamic system excited by non-gaussian inputs usingkth order (k> 2) cumulants of input and output signals contaminated by additive (possibly coloured) gaussian noise. The parameter estimates obtained by this method are proved to be consistent under weak conditions. This method has an on-line algorithm for computing the parameter estimates, just like the least-squares method. A simulation example is included to demonstrate the effectiveness of this method.