Quasiperiodic binary tilings B1, B2 and B3 can be viewed as the superposition of two fivefold quasiperiodic tilings. Two fivefold quasiperiodic tilings F1 and F2 related to the binary tiling B3 are discussed. The subunits of the Al‒Mn‒Pd decagonal quasicrystal are consistent with the tiles in the fivefold quasiperiodic tilings. An ideal quasilattice of the Al‒Mn‒Pd decagonal quasicrystal can be regarded as an alternating stacking of the F1 and F2 quasilattices.