Iterated weighted least squares (IWLS) is investigated for estimating the regression coefficients in a linear model with symmetrically distributed errors. The variances of the errors are not specified; it is neither assumed that they are unknown functions of the explanatory variables nor that they are given in some parametric way IWLS is carried out in a random number of steps, of which the first one is OLS. In each step the error variance at time t is estimated with a weighted sum of m squared residuals in the neighbourhood of t and the coefficients are estimated using WLS. Furthermore an estimate of the covariance matrix is obtained. If this matrix is somehow smaller than the one before, a new step is carried out unless an upper bound has been reached.