In order to characterize the initial phase of the divergent detonation wave in PBX, a hemispheric explosive sample was initiated by a long cylindrical charge of the same explosive. The tested PBX is composed of 85 wt% of RDX and 15 wt% of binder based on HTPB. This PBX-RDX presents an effective density of 1.57 g/cm(3), and a detonation velocity of 7.90 mm/mus. An optical method, based on ribbon consisting of 64 optical fibers (each fiber of 250 W diameter) and connected to a fast electronic streak camera, allows the measurement of the detonation velocity in the PBX hemisphere as a function of the run distance R along several directions characterized by different angles with the axis of the sample. The obtained results, presented as radius-time and velocity-radius functions, show the evolution of a divergent detonation wave in its run up to a radius equal to 33 - 34 mm (6.6 - 6.8 times more than the diameter of the initiator). The real shape of the divergent detonation wave was obtained, and it was found significantly different from the ideal Huygens model. The measurements of the pressure of a shock wave induced either by the divergent detonation wave or by a positive constant curvature detonation wave (detonation in a long cylindrical PBX charge) in an inert standard barrier show the existence of significant differences between them which can reach values up to 2.8 times less, in their amplitudes.