The attenuation of shear waves in the crust is estimated, for frequencies between 1.5 and 12.0 Hz, by applying a single-station method based on the rate of decay of the S-wave to coda-wave amplitude ratio with distance. The data used come from local earthquakes that occurred in the Thessaloniki area, northern Greece, during the period 1983 through 1989 and were recorded by the telemetered network of the Geophysical Laboratory of the University of Thessaloniki. The Qs values obtained are 115, 244, 477, and 755 for 1.5, 3.0, 6.0, and 12.0 Hz, respectively. These values are very close to the coda Q values estimated for the same area using the S-to-S single scattering model for lapse times between 30 and 100 sec but they are higher than the coda Q values for lapse times between 10 and 30 sec. The estimated Qs is found to be strongly frequency dependent, proportional to f0.91, which is very close to the frequency dependence of the coda Q.