To provide a transom structure serving also as a mullion of novel design capable of securing certain strength while avoiding variations among finished products, and a method of constructing it.

The mullion or transom structure includes a mullion 4 or a transom member 25 by which a rectangular frame surrounded by two jamb members 1 and 1, a lintel member 2 and a threshold member 3 is divided either horizontally or vertically or both, with sashes 5 fitted into rectangular sections divided from one another. The mullion or transom is in the form of a bar integrally molded from synthetic resin and having a uniform cross section. A long metallic member of rectangular cross section is either insert molded into the mullion 4 and the transom member 25 as a core 7 or is inserted into a core portion after being molded.