In the study of Hardy e al. (1989) the average pattern of auroral ion precipitation was determined as a function of corrected geomagnetic latitude, magnetic local time (MLT), and Kp using data from the SSJ/4 detectors on the satellites of the Defense Meteorological Satellite Program (DMSP). One product of this study was a set of hemispheric maps of the integral number flux and integral energy flux of the precipitating ions for each of seven levels of activity as defined by Kp. In order to facilitate the use of these maps in magnetospheric, ionospheric, and thermospheric models, they have been fit to a functional form. To accomplish this, the latitudinal variation in the integral energy and number flux in each of 48 helaf-hour MLT bins of the original statistical study, for each Kp level, was fit to a general form of the Epstein function. This functional form was chosen since it fits well the asymmetric shape of the latitudinal profile of the integral energy and number flux. The Epstein function fits to the latitudinal profiles require six variables in each MLT zone. To further reduce the number of variables needed to specify a map, the MLT variation of each of the six variables was expanded as a sixth-order Fourier series with 13 coefficients. The resulting fit reproduces well the original statistical data. The distribution of differences between the original data and the fit normalized to the original data shows agreement that is generally better than 25% for both the integral energy and number flux. ¿ American Geophysical Union 1991