A two-photon laser-induced fluorescence study on the transport of ground-state atomic hydrogen in a supersonic plasma jet, generated from an Ar-H (2) mixture, reveals an unexpected shock pattern. Whereas both the axial-velocity profile and the temperature profile of hydrogen atoms along the jet centerline can be interpreted in terms of a supersonic expansion of an Ar-H gas mixture, the H-atom density profiles do not satisfy the well established Rankine-Hugoniot relation leading to a nonconservation of the forward flux. The experimental results show that H atoms escape from the supersonic expansion by a diffusion process due to strong density gradients between the core of the jet and its vicinity.