This paper presents a procedure for estimating the components in an economic time series assuming a constant seasonal component and a trend which may be estimated locally by a polynomial. The procedure is to estimate the trend and seasonal components for each consecutive two-year time span of quarterly data using conventional least-square techniques. Thus, for each quarter in the series, except the first seven and last seven, there are eight estimates for each of these components. A weighted average of these estimates is obtained using weights such that the variance of the average is a minimum. This procedure is used to adjust male unemployment in the United States for seasonal variation, and the results compare favorably with the official adjustment of the Bureau of Labor Statistics.