Expressions for the shape factors of the Lth degree of forbidden $\beta $-transition were given by Greuling (1942) for the pure interactions and by Pursey (1951) for different mixtures of the pure forms. The same results have been derived here by a method due to Spiers & Blinstoyle (1952) and formulated neatly in terms of three parameters, (a) $\xi $ giving the spatial covariance, (b) $\eta $ giving the spatial parity and (c) $\zeta $ giving the space-time parity. The results readily point out that the correct form of interaction in the $\beta $-processes is either a STP combination or a VA combination. It has been concluded that the proper way of setting up the $\beta $-interaction is to require that all the Dirac covariants, whose scalar products appear in the Hamiltonian, must behave in the same way under space-time reflexion. A brief sketch of the principal mathematical tools required in the method of Spiers & Blinstoyle has also been given.