We prove that all harmonic maps from $ {{\mathbb{R}}^{2}} $ to $ {{\mathbb{S}}^{2}} $ with finite energy are nondegenerate. That is, for any harmonic map $ u $ from $ {{\mathbb{R}}^{2}} $ to $ {{\mathbb{S}}^{2}} $ of degree $ m\in\mathbb Z $, all bounded kernel maps of the linearized operator $ L_u $ at $ u $ are generated by those harmonic maps near $ u $ and hence the real dimension of bounded kernel space of $ L_u $ is $ 4|m|+2 $.
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