Using the fixed point method an implicit function theorem was proved. This theorem is a generalization of theorem 3 in [1]. \emph{Theorem} Let $f$ be defined and continuous in a neighborhood $V(x_0y_0) \subset E\times F$ and maps $V$ into $F$ so that the following conditions are satisfied 1. $f(x_0y_0)=0$ 2. for every $(x_0y_0)\in V(x_0y_0)$ there exists $f_y(x,y)$ in the Frechet sense, $f_y(x,y) \in\mathcal L\varphi(E,F)$ and the mapping $(x,y)\to f_y(x,y)$ is continuous in the point $(x_0y_0)$. 3. left inverse $[f_y(x_0y_0)]^{-1}l$ (or right inverse) is in $\mathcal L\psi(F,F)$ where the mapping $\varphi_0\psi=0$ has the following property: for every $\beta\in\mathcal B$ there exist $m(\beta)\geq0$ and $\delta(\beta)\in\mathcal B$ so that $|y|\theta k(\beta)\leq m(\beta)|y|\delta(\beta)k=1,\ldots y\in F$. Then $f(x,y)=0\Leftarrow>y=g(x)$ for evey $(x,y)\subset(x+H)\times(y_0+K)$ (see (4)) and $g$ is continuous on $(x_0+H)$.