The characterization of long-range correlations and fractal properties of DNA sequences has proved to be adifficult though rewarding task mainly due to the mosaic character of DNA consisting of many patches of various lengthswith different nucleotide constitutions.In this paper we investigate statistical correlations among different positions in DNAsequences using the two-dimensional DNA walk.The root-mean-square fluctuation F(l)is described by a power law.Theautocorrelation function C(l),which is used to measure the linear dependence and periodicity,exists a power law ofC(l)-l~(-μ).We also calculate the mean-square distancealong the DNA chain,and it may be expressed as-l~(?)with 2>γ>1.Our investigations can provide some insights into long-range correlations in DNA sequences. The characterization of long-range correlations and fractal properties of DNA sequences has proved to be adifficult though rewarding task due due to the mosaic character of DNA consisting of many patches of various lengths with different nucleotide constitutions.In this paper we investigate statistical correlations among different positions in DNAsequences using the two-dimensional DNA walk.The root-mean-square fluctuation F (l) is described by a power law. Theautocorrelation function C (l), which is used to measure the linear dependence and periodicity, exists a power law ofC (l) -l ~ (-μ) .We also calculate the mean-square distance along the DNA chain, and it may be expressed as γ> 1.Our investigations can provide some insights into long-range correlations in DNA sequences.