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For a central system uniformly coupled to a XY spin-1/2 bath in a transversefield, we explicitly calculate the Loschmidt echo(LE) to characterizedecoherence quantitatively. We find that the anisotropy parameter $\gamma $affects decoherence of the central system sensitively when $\gamma \in [0,1]$%, in particular, the LE becomes unit without varying with time when $\gamma =0$, implying that environment-induced decoherence vanishes . Some other cases inwhich the LE is unit are discussed also.Comment: 4 pages, 2 figure

Decoherence of a central quantum system coupled to anXYspin chain