A two step method is proposed to reduce colored noise for chaotic data in the local phase space. With the observation that the energy of colored noise is mainly distributed in a low dimensional subspace, a noise dominated subspace is first estimated by the energy distribution of colored noise. At step 1, for the reference phase point, the components projected into the noise dominated subspace are deleted and the enhanced data are reconstructed with the remaining components. The residual error of the output of step 1 tends to distribute on each direction uniformly. So at step 2, the local projection method is further applied to the output of step 1, treating the residual error as white noise. Experiments show that our method performs well in eliminating colored noise for chaotic data.