  For a central system uniformly coupled to a XY spin-1/2 bath in a transverse
field, we explicitly calculate the Loschmidt echo(LE) to characterize
decoherence 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 in
which the LE is unit are discussed also.
