We propose a new technique to analyze trends in moments of the statistical distribution of climatic indices. A standard approach (linear regression, polynomial fit, or least squares fit to a specific function) is first used to evaluate the trend in the expected value of an observed climatic index. The innovation here is that after the trend in the expected value is subtracted from the observed time series, we calculate the time series of the squares, cubes, fourth powers, and any other combination of the residuals (anomalies). Then we apply the same standard trend analysis technique to the time series of these new variables. This technique can be used to determine whether the observed climate is getting more or less variable. The observed 1901--2000 New York City sea level variations, U.S. annual average precipitation, U.S. annual averages of the Modified Palmer Drought Severity Index, All-India Monsoon Rainfall Index, and Southern Oscillation Index are used to illustrate the technique. There are no significant trends in variability of any of these climatic indices for the past 100 years.