Changes in the variance of streamflow over time may possibly be caused by land cover changes or climate changes. Knowledge of these possible changes in the time series structure is desirable for validation of modeling efforts; detection is not always straightforward, however. We present the use of a wavelet-based statistical test for the detection of changes in the variance of a time series applied to records of streamflow from 12 rivers in the United States from the period 1954--1999. The test is able to show during which time periods and at what wavelet scales changes in the variance are taking place. It is found that the major similarities in variance change for all the streamflow time series exist when the largest time domain wavelet is used and also when a wavelet of the second largest frequency scale is used. Sampling considerations prevent exact localization of the time and frequency of the change(s). Results of the test indicate that for the data analyzed in this study a change in the variance of the streamflow time series most likely did take place over the time period examined.