This paper presents a novel approach to accurately extract the resonant modes of a mode-stirred Reverberation Chamber (RC) from measured transmission coefficient. This approach neither requires measurements with a fine stirrer rotation step nor assumes the pole continuity over a stirrer rotation. First, the number of modes to be extracted by the Matrix Pencil method needs to be overestimated in order to obtain most of the true (physical) modes with high accuracy. As this overestimation also implies the extraction of many spurious modes, the second step consists in automatically filtering these spurious modes based on a time-window increasing technique post-process without a priori information. Performances of the introduced technique are first shown on a didactic example, especially in the presence of noise, and its limitations when increasing the modal overlap are investigated. Results obtained from measurement performed in a chaotic RC are then presented. The introduced approach allows extracting all the true cavity modes from measurement data while keeping the percentage of spurious modes below 3.5 %.