First principles total energy calculations were performed to investigate the Si(0 0 1)-(3×4)–Al reconstruction obtained when Al is deposited at high temperatures. Three different models were considered in the optimization of the surface atomic structure. The first one was based in the model schematically proposed by Zhu et al. to explain their STM images of Al on Si(0 0 1). The other two models, due to Zotov et al. [Phys. Rev. B 57 (1998) 12492] and Bunk et al. [Appl. Surf. Sci. 123–124 (1998) 104] respectively, have been previously proposed to explain a similar reconstruction for the Si(0 0 1)–In system. Results show that the structure based on Bunk's et al. model yields the most stable configuration. The formation of pyramid-like Al-subunits is clearly manifested with a trimer on top. The trimer is formed by a Si atom occupying the highest vertical position and bound to two Al atoms with lower vertical positions. Local density of state images were calculated for this model and compared with the experimental STM measurement of Zhu et al. [Phys. Rev. B 59 (1999) 9760] giving excellent results.