In this work we defined a generalized Finsler space $(\mathbb{GF_N})$ as $2N$-dimensional differentiable manifold with a non-symmetric basic tensor $g_{ij}(x, \dot{x}),$ which applies that $\gs ij_{\underset {\theta} |m}(x,\dot{x})=0,\mbox{ } \theta=1,2.$ Based on non-symmetry of basic tensor, we obtained ten Ricci type identities, comparing to two kinds of covariant derivative of a tensor in Rund's sense. There appear two new curvature tensors and fifteen magnitudes, we called ``curvature pseudotensors''.