The Si(001) surface deoxidized by short annealing at T ~ 925°C in the ultrahigh vacuum molecuar beam epitaxy chamber has been in situ investigated using high-resolution scanning tunneling microscopy (STM)and redegreesected high-energy electron diffraction (RHEED. RHEED patterns corresponding to (2 × 1) and (4 × 4) structures were observed during sample treatment. The (4 × 4) reconstruction arose at T ≲ 600°C after annealing. The reconstruction was observed to be reversible: the (4 × 4) structure turned into the (2 × 1) one at T ≳ 600°C, the (4 × 4) structure appeared again at recurring cooling. The c(8 × 8) reconstruction was revealed by STM at room temperature on the same samples. A fraction of the surface area covered by the c(8 × 8) structure decreased, as the sample cooling rate was reduced. The (2 × 1) structure was observed on the surface free of the c(8 × 8) one. The c(8 × 8) structure has been evidenced to manifest itself as the (4 × 4) one in the RHEED patterns. A model of the c(8 × 8) structure formation has been built on the basis of the STM data. Origin of the high-order structure on the Si(001) surface and its connection with the epinucleation phenomenon are discussed.PACS 68.35.B-·68.37.Ef·68.49.Jk·68.47.Fg.