[en] The Transition Radiation Detector of the ZEUS experiment at DESY is one of its main instruments for electron identification. It started to operate partly in 1993 and for the first time with its four modules in 1994. One of its main features is a Time Expansion Chamber to detect the transition radiation of electrons together with the ionisation energy loss of the particle tracks. The first data taken under realistic environmental conditions served as tool to find appropriate running conditions and procedures for data treatment. The main aim however was to show that the detector is sensitive to electrons and to evaluate its rejection power. This analysis describes the on-line and off-line data processing required to exploit the information contained in the raw data. Concepts for detector cross channel calibration and signal recombination are presented. The effect of different running conditions is discussed. To determine the rejection power a data selection was performed extracting electrons and hadrons using all means except the TRD. The response of the TRD to these data samples was compared and a clear sensitivity for electrons was found. Using different likelihood methods values for separation power are derived. The hadron suppression obtained at 90% electron efficiency is - for momenta from 1 to 3 GeV/c - between 27% to 10%, which is already close to the design/test chamber results of 9% to 1.7%. As a projection for close-to-optimum running conditions a hadron suppression from 12% to 2% was obtained. (orig.)