The attenuation function, log A(subscript o)(△), used in the calculation of local magnitude is derived for the Taiwan area. The simulated Wood-Anderson seismograms are constructed by using digital three-components short-period seismogram of the Central Weather Bureau Seismic Network, (CWBSN). The decay of peak amplitude with distance is the attenuation characteristic of seismic energy. Also, it essentially represents the distance correction term, log A(subscript o) (△), after a proper normalization. Considering the focal depth of earthquakes in the Taiwan area, the log A(subscript o)(△)functions are: (The equation is abbreviated) for shallow earthquakes (focal depth, h≤35 km) and log A(subscript o)(△)=-0.00326R-0.83 logR-1.01 for deep earthquakes (h>35 km) where △ is epicentral distance, R((The equation is abbreviated)) is the hypocentral distance. Results also show that the local magnitude of a deep earthquake is underestimated by using the Richter's log A(subscript o)(△) values (1935, 1958) with comparison to the M(subscript L) value obtained from the revised log A(subscript o)(△)values of this study. By applying the revised attenuation function, a compatible local magnitude can be calculated from the strong motion data. The conversion of duration magnitude, M(subscript D) which is currently used in the Taiwan area, to M(subscript L)is in the form: M(subscript L)=1.12 M(subscript D)+0.03±0.21