This paper presents a new topology for a high voltage 50kV, high frequency (HF) 20kHz, multi-cored transformer. The transformer is suitable for use in pulsed power application systems. The main requirements are: high voltage capability, small size and weight. The HV, HF transformer is a main critical block of a high frequency power converter system. The transformer must have high electrical efficiency and in the proposed approach has to be optimized by the number of the cores. The transformer concept has been investigated analytically and through software simulations and experiments. This paper introduces the transformer topology and discusses the design procedure. Experimental measurements to predict core losses are also presented.