The atomic masses of the neutron-deficient radioactive rubidium isotopes 74−77,79,80,83Rb have been measured with the Penning trap mass spectrometer ISOLTRAP. Using the time-of-flight cyclotron resonance technique, relative mass uncertainties ranging from 1.6×10−8 to 5.6×10−8 were achieved. In all cases, the mass precision was significantly improved as compared with the prior Atomic-Mass Evaluation; no significant deviations from the literature values were observed. The exotic nuclide 74Rb with a half-life of only 65 ms, is the shortest-lived nuclide on which a high-precision mass measurement in a Penning trap has been carried out. The significance of these measurements for a check of the conserved-vector-current hypothesis of the weak interaction and the unitarity of the Cabibbo-Kobayashi-Maskawa matrix is discussed