$f$-manifolds have been studied by various authors including Blur D. [1], Endo H. [2], Yano K. [5] and the integrability conditions of this structure [6]. Singh K. and Srivastava R. in [4] prove a number of theorems involving the fundamental tensor for almost Hermitian manifolds with torsion and study a torsion preserving conformal diffeomorphism. The paper studies the conformal diffeomorphism between two Riemannian $f$-manifolds and the Nijenhuis tensor on such manifolds. The result is obtained: The structure $f'$ on $\mathcal M'^n$ is integrable iff and only iff the structure $f$ on $\mathcal M^n$ is integrable, where $\mathcal M^n$ and $\mathcal M'^n$ are conformal diffeomorphically Riemannian $f$-manifolds with the structure tensors $f$ and $f'$, respectively.