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In this paper we study the {\\it generalized quadratic covariation} $[f(B^H),B^H]^{(W)}$ defined by $$ [f(B^H),B^H]^{(W)}_t=\\lim_{\\epsilon\\downarrow 0}\\frac{2H}{\\epsilon^{2H}}\\int_0^t\\{f(B^{H}_{s+\\epsilon})-f(B^{H}_s)\\}(B^{H}_{s+\\epsilon}- B^{H}_s)s^{2H-1}ds, $$ where the limit is uniform in probability and $x\\mapsto f(x)$ is a deterministic function. 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