The author considers the construction of the coincidence degree for the perturbation of Fredholm operators introduced by J. Mawhin [J. Differ. Equations 12, 610-636 (1972; Zbl 0244.47049)]. The aim of the paper is to provide a definition which is based on the essential assumptions. The author shows that the definition of the coincidence degree requires only the normed structure of the source space so that the target space can be taken as an arbitrary real vector space.