This prefabricated locking quoin block is used to construct the surface of buildings. The surface of the block has decorative portions resembling brick, stone, wood, or other construction materials. Preferably the surface of each block has both a raised and a recessed decorative portion, so as to form, when assembled, a quoin corner assembly resembling sawn or quarried stone blocks. Installers can attach the assemblies to conventional building structures and install cladding materials such as vinyl siding without needing to alter the blocks other than to adjust the base block for height. The block includes wedge locks to securely connect adjacent blocks matingly to each other. Installers thereby are able to assemble a secure stack of quoin corner blocks and attach it to a building with few additional steps, saving time, labor, and cost in construction.