In this paper we present a new criterion on characterization of real inner product spaces. We conclude that a real normed space $(X, \|\cdot\|)$ is an inner product space if $$\sum_{\varepsilon_i \in \{-1,1\}} \left\|x_1 + \sum_{i=2}^k\varepsilon_ix_i\right\|^2=\sum_{\varepsilon_i \in \{-1,1\}} \left(\|x_1\| + \sum_{i=2}^k\varepsilon_i\|x_i\|\right)^2\,,$$ for some positive integer $k\geq 2$ and all $x_1, \ldots, x_k \in X$. Conversely, if $(X, \|\cdot\|)$ is an inner product space, then the equality above holds for all $k\geq 2$ and all $x_1, \ldots, x_k \in X$.

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