We studied the atomic structure of the Si(00l)-c(4x12)-Al surface, which appears in scanning tunneling microscopy (STM) images as an array of clusters in the four-fold direction. Transmission electron diffraction (TED) patterns showed (h/4,k/12) fractional-order spots after depositing about four monolayers of aluminum on clean Si(00l) surfaces at a substrate temperature of 600 o C. A model, which accords with the TED intensity and the observed STM images, consists of a periodical terrace-and-trench geometry in the 12-fold direction. In the four-fold direction, an aluminum ad-dimer is adsorbed every 4a distance (a=0.384nm) on the terraces terminated by double-height steps, making up the cluster array corresponding to bright protrusions in STM images. In addition to ad-dimers, rebonded atoms at the double-height step edge and zigzag isolated dimers in the trench are found to be the building blocks of the c(4x12) structure.