Protostellar jets appear at all stages of star formation when the accretion process is still at work. Jets travel at velocities of hundreds of km s -1, creating strong shocks when interacting with the interstellar medium. Several cases of jets have been detected in X-rays, typically showing soft emission. For the first time, we report evidence of hard X-ray emission possibly related to non-thermal processes not explained by previous models of the post-shock emission predicted in the jet/ambient interaction scenario. HH 80 is located at the south head of the jet associated with the massive protostar IRAS 18162-2048. It shows soft and hard X-ray emission in regions that are spatially separated, with the soft X-ray emission region situated behind the region of hard X-ray emission. We propose a scenario for HH 80 where soft X-ray emission is associated with thermal processes from the interaction of the jet with denser ambient matter and hard X-ray emission is produced by synchrotron radiation at the front shock.