Linear　discriminant　analysis　(LDA)　is　awell-known　supervisedmethod　for　dimensionality　reduction　in　which　the　global　structure　of　data　can　be　preserved.　The　classical　LDA　is　sensitive　to　the　noises,　and　the　projection　direction　of　LDA　cannot　preserve　the　main　energy.　This　article　proposes　a　novel　feature　extractionmodel　with　l2,1　norm　constraint　based　on　LDA,　termed　as　RALDA.　This　model　preserves　within-class　local　structure　in　the　latent　subspace　according　to　the　label　information.　To　reduce　information　loss,　it　learns　a　projection　matrix　and　an　inverse　projection　matrix　simultaneously.　By　introducing　an　implicit　variable　and　matrix　norm　transformation,　the　alternating　direction　multiple　method　with　updating　variables　is　designed　to　solve　the　RALDA　model.　Moreover,　both　computational　complexity　and　weak　convergence　property　of　the　proposed　algorithm　are　investigated.　The　experimental　results　on　several　public　databases　have　demonstrated　the　effectiveness　of　our　proposed　method.