Reducing the number of secondary data used to estimate the Covariance Matrix (CM) for Space Time Adaptive Processing (STAP) techniques is still an active research topic. Within this framework, the Low-Rank (LR) structure of the clutter is well-known and the corresponding LR STAP filters have been shown to exhibit a smaller SNR loss than classical STAP filters, 2r secondary data (r is the clutter rank) instead of 2m (m is the data size) is needed to reach a 3dB SNR loss. By using other features of the radar system, other properties of the CM could be exploited to further reduce the number of secondary data: this is the case for active systems using a symmetrically spaced linear array with constant pulse repetition interval. In this context, we propose to combine the resulting persymmetric property of the CM and the LR structure of the clutter to perform the CM estimation. In this paper, the resulting STAP filter is shown, both theoretically and experimentally, to exhibit good performance with fewer secondary data: 3dB SNR loss is achieved with only r secondary data.