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In this study, the effects of non-side-looking airborne radar clutter dispersion for space-time adaptive processing (STAP) is considered. An efficient adaptive algorithm is presented for mitigating the clutter range-dependence performance loss by pre-eliminating the short-range clutter before clutter covariance estimation. Owing to the improved training sample selection strategy, this approach is able to reduce the adaptive degrees of freedom into elevation sum and difference beams, thereby improving the convergence rate and the adaptive beam pattern. Simulation results are demonstrated that the clutter range dependence can be significantly alleviated by using this proposed approach, thus the STAP performance is enhanced. In addition, this approach is computationally efficient, and favorable for engineering application.