Radiosity methods produce very striking interreflection effects for an enclosed diffuse environment. The quality of the images synthesized by radiosity methods varies depending on the calculation accuracy of the form factor, which is a geometric factor depending only on the relative orientation and position between two surfaces. Hemicube projection has been proposed to check the visibility between surfaces and calculate the form factor efficiently, but there is no analytical solution due to the double area integration. This paper presents a new form of the form factor and gives a theoretical derivation from the point view of illumination engineering. The new form factor contains only one area integration, so it can be computed analytically. An energy conservation condition applies to verify the correctness of the new model. The error introduced by using reciprocity as part of the form factor calculation has been eliminated, but the principle of reciprocity is maintained. The hemisphere projection method is used as an analytical solution of the new form factor. Finally, images generated by the new radiosity method are presented. Interreflection effects can be clearly seen around the intersection of the surfaces.