Abstract: A corner trim member for use in drywall or other sheet wall construction. The cover trim has at least two wall members joining each other along a common edge, so that each wall member can overlay a corresponding corner portion of mutually-orthogonal drywall panels. Each side member of the trim has a relatively thick portion extending from a corner common to the wall members, and a second portion of reduced thickness relative to the first portion. The difference in thicknesses of the two wall portions is substantially equal to the thickness of a conventional cornerbead member with which the trim is used. Those cornerbead members overlay the relatively thin portion of the trim, so that the cornerbead is substantially flush with the relatively thick portions of the cap. The present trim thus provides structural underpinning for drywall finishing mud applied to a wall corner covered by the trim.