Stars form in the cold dense cores of interstellar molecular clouds and the detailed knowledge of the spectrum of masses of such cores is clearly a key for the understanding of the origin of the IMF. To date, observations have presented somewhat contradictory evidence relating to this issue. In this paper we propose to derive the mass function of a complete sample of dense molecular cores in a single cloud employing a robust method that uses uses extinction of background starlight to measure core masses and enables the reliable extension of such measurements to lower masses than previously possible. We use a map of near-infrared extinction in the nearby Pipe dark cloud to identify the population of dense cores in the cloud and measure their masses.