Abstract: A footing is poured with an inner row and an outer row of upwardly projecting tie legs set therein. An inner course and an outer course of blocks having appropriate downwardly opening sockets are respectively placed on the footing, with the tie legs being received in those sockets. The blocks also have upwardly opening sockets. Downwardly projecting legs of H-shaped ties are mounted in those sockets, each tie uniting an inner block and an outer block in the same course. The upwardly projecting legs of these H-shaped ties then receive the downwardly opening sockets of the next upper inner and outer courses of blocks, and so on until the desired number of block courses are in place. No mortar is used in setting the first course on the foundation or in setting each succeeding course. However, when the courses are in place, concrete or equivalent settable composition is poured in the space between the inner and outer block rows to fill the space and thus create an integral wall.