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In this article, we construct a new metric $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}  \over G}  = {}^R\nabla  + \sum\limits_{i,j = 1}^m {a^{ji}} \delta {p_j}\delta {p_i}$  in the cotangent  bundle, where ${}^R\nabla $ is the  Riemannian extension and  $ a^{ji}$ is a symmetric (2,0)-tensor field on a differentiable manifold.

Cotangent bundle, Riemannian extension, geodesic, para-Nordenian metric

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