  Let $ H_1,\dots,H_{2n+2}$ be \emph{generic} $(2n+2)$ hyperplanes in
$\mathbb{P}^n.$ It is proved that if meromorphic maps $ f $ and $ g $ of
$\mathbb{C}^m $ into $\mathbb{P}^n $ satisfy $ f^*(H_j)=g^*(H_j)$ $(1\leq j\leq
2n+2)$ and $ g $ is algebraically non-degenerate then $ f=g.$ This result is
essentially implied by the proof of Hirotaka Fujimoto in papers [Nagoya Math.
J., 1976(64): 117--147] and [Nagoya Math. J., 1978(71): 13--24]. This note
gives a complete proof of the above uniqueness result.
