A discrete Point Spread Function (PSF) is a sampled version of a continuous two-dimensional PSF. The shape information about the photon scattering pattern of a discrete PSF is typically encoded using a numerical table (matrix) or a FITS image file. MATPHOT shifts discrete PSFs within an observational model using a 21-pixel- wide damped sinc function and position partial derivatives are computed using a five-point numerical differentiation formula. MATPHOT achieves accurate and precise stellar photometry and astrometry of undersampled CCD observations by using supersampled discrete PSFs that are sampled two, three, or more times more finely than the observational data.