Catalyzes the reversible oxidation of malate to oxaloacetate. (S)-malate + NAD(+) = H(+) + NADH + oxaloacetate kcat is 197 sec(-1) with oxaloacetate as substrate (in the presence of 2 M NaCl). kcat is 69 sec(-1) with oxaloacetate as substrate (in the presence of 4 M NaCl). Homotetramer; arranged as a dimer of dimers. The quaternary structure is stabilized by chloride ions bound between the subunits. This may be an adaptation to the halophilic environment. Belongs to the LDH/MDH superfamily.