A four-chamber Otto-cycle rotary engine, the Szorenyi Rotary Engine, has been developed by the Rotary Engine Development Agency in Melbourne, Australia. The engine has been awarded a US patent. The geometric shape of the engine rotor is a rhombus which deforms as it rotates inside the contour of a mathematically defined stator. The resulting engine design has a four-segment hinged rotor which creates four combustion chambers. Each chamber produces the four phases of the Otto cycle for every rotation of the rotor. The result is an engine which is similar in operation and size to a Wankel engine, but with four times the power density. The Szorenyi engine could be used in all current applications of Wankel and reciprocating engines. The paper follows the development of the Szorenyi engine. It describes the derivation of the mathematical formula of the stator profile and shows that the profile can be varied to optimise the combustion chamber shape and hence engine performance. The paper traces the engineering solutions to create a four-segment hinged rotor with incorporated seals. The successful proof-of-concept engine test is described, and the subsequent tear-down and detail design improvements that were made. The ideal mathematical modelling of the engine, conducted by RMIT University (Melbourne), is described. The modelling compared the Szorenyi engine with an equivalent reciprocating engine. The engines' combustion chamber geometries were modelled and the fuel burn was analysed using a Wiebe function. The paper shows that the slower rate of change of combustion chamber volume of the Szorenyi engine either side of top dead centre results in it having 0.45% higher thermal efficiency than the equivalent reciprocating engine and 0.35% higher than the equivalent Wankel engine. The paper discusss the further development planned for prototype engine testing and more advanced computer modelling.