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We report the discovery of a substellar companion around the giant star HIP 67537. Based on precision radial velocity measurements from CHIRON and FEROS high-resolution spectroscopic data, we derived the following orbital elements for HIP 67537 b: m(b) sin i = 11.1(-1.1)(+0.4) M-jup, a = 4.9(-0.13)(+0.14) AU and e = 0.59(-0.02)(+0.05). Considering random inclination angles, this object has greater than or similar to 65% probability to be above the theoretical deuterium-burning limit, thus it is one of the few known objects in the planet to brown-dwarf (BD) transition region. In addition, we analyzed the HIPPARCOS astrometric data of this star, from which we derived a minimum inclination angle for the companion of similar to 2 deg. This value corresponds to an upper mass limit of similar to 0.3 M-circle dot, therefore the probability that HIP 67537 b is stellar in nature is less than or similar to 7%. The large mass of the host star and the high orbital eccentricity makes HIP 67537 b a very interesting and rare substellar object. This is the second candidate companion in the brown dwarf desert detected in the sample of intermediate-mass stars targeted by the EXoPlanets aRound Evolved StarS (EXPRESS) radial velocity program, which corresponds to a detection fraction of f = 1.6(-0.5)(+2.0)%. This value is larger than the fraction observed in solar-type stars, providing new observational evidence of an enhanced formation efficiency of massive substellar companions in massive disks. Finally, we speculate about different formation channels for this object.