We present a new measurement of the antiproton-to-proton abundance ratio, pbar/p, in the cosmic radiation. The HEAT-pbar instrument, a balloon borne magnet spectrometer with precise rigidity and multiple energy loss measurement capability, was flown successfully in Spring 2000, at an average atmospheric depth of 7.2 g/cm(2). A total of 71 antiprotons were identified above the vertical geomagnetic cutoff rigidity of 4.2 GV. The highest measured proton energy was 81 GeV. We find that the pbar/p abundance ratio agrees with that expected from a purely secondary origin of antiprotons produced by primary protons with a standard soft energy spectrum.