Abstract: Reduced transition strengths of the deexciting transitions from the first two excited states in Ar-33 were measured in a relativistic Coulomb excitation experiment at the GSI Helmholtz center. The radioactive ion beam was produced by fragmentation of a primary Ar-36 beam on a Be-9 target followed by the selection of the reaction product of interest via the GSI Fragment Separator. The (33A)r beam hit a secondary Au-197 target with an energy of approximately 145 MeV/nucleon. An array of high-purity germanium cluster detectors and large-volume BaF2 scintillator detectors were employed for gamma-ray spectroscopy at the secondary target position. The Lund-York-Cologne Calorimeter was used to track the outgoing ions and to identify the nuclear reaction channels. For the two lowest energy excited states of Ar-33 the reduced transition strengths have been determined. With these first results the T-z = -3/2 nucleus Ar-33 is now, together with Na-21 (T-z = -1/2), the only neutron-deficient odd-A sd shell nucleus in which experimental transition strengths are available. The experimental values are compared to results of shell-model calculations which describe simultaneously mirror-energy differences and transition-strength values of mirror pairs in the sd shell in a consistent way.