At the previous AFMC, the background for expecting a departure from Rankine-Hugoniot theory at the base of the reflected shock wave in weak Mach reflection was exposed. The results of some pertinent experiments performed in the supersonic wind tunnel were then presented. They confirmed the hypothesised irregular behaviour. In the present contribution, the elaboration of a theory of transgressed shock wave properties is presented. This concept enables to calculate the modified jump process. It fully accounts for the known experimental observations. It is the unyielding boundary conditions that prevail beyond regular reflection which force this remarkable deviation from the classical shock wave theory to take place