The present invention includes a method and a unit for a masonry wall system, each unit comprising a face shell wherein the interior surface has a transverse axis running from the top surface to the bottom surface of the face shell, and one or more webs having a front end and a rear end, wherein the rear end of each web is integral with or attached to the interior surface of the face shell along the transverse axis. The method for wall construction further comprising positioning one or more vertical reinforcement rods or tendons with one end embedded in a wall-foundation and laying a layer wall units on the wall-foundation such that the one or more webs of the layers of wall units are aligned, and the vertical reinforcement rods or tendons run through or are adjacent to the webs of the wall units.