A system of blocks is configured to be compatible with each other in the construction of a columnar structure. Each block has four faces and all four faces may generally have the same dimensions. The width of the blocks may generally be about twice their height. The faces of the block also may contain a slot to add an aesthetic appearance to the column. The blocks have certain constructions features that mate with specially constructed brackets in attaching a fence panel to the completed column.The blocks have interlocking elements or projections that permit positive connection between courses of blocks. Projections of one block extend into the core another block. Adjacent blocks can be rotated 90 degrees relative to each other about a vertical axis of each block with each course. The blocks can be used to construct a column that is easy to install and structurally sound.