This paper deals with the Hilbert space valued processes equivalent to a Wiener process in the sense of being equivalence transformations of the Wiener process. It is being proved that each equivalence transformation of the Wiener process can be presented in the following form $X(t)=W(t)-\int_0^t Y(s)\,ds$ and separately $X(t)=W(t)-\int^t_0\int^T_0l(s,x)\,dW(x)\,ds$. The obtained results are different forms of representation and they make a very significant step in solving the problem of canonical representation (Ilida--Cramer) of Hilbert space valued processes equivalent to the Wiener process without the use of the Factorization theorem