redshift, such as z ∈ (0 , 0 . 9) and z ∈ (0 , 1 . 8). In such regions, the width of each redshift bin is small and the linear expansion could be a better approximation of w$_{de}$ ( z ) than a constant in each bin. When fitting with the observational data, we leave the divided positions of bins z$_{i}$ as free parameters. Since the linear function is monotonic, the best-fitted z$_{i}$ can represent the turning points of w$_{de}$ ( z ), where w$_{de}$ ( z ) is not linear enough or even non-monotonic (i.e., where d $^{2}$w$_{de}$ /dz 2 departs from zero substantially). Actually we do find some turning points of w$_{de}$ from observational data, and the constructed w$_{de}$ ( z ) just turns its evolution direction at the best-fitted positions of z$_{i}$ . In this way, we only need to divide redshift into a few bins, the turning points are natural divided points of redshift and w$_{de}$ between two nearby points can be accurately reconstructed by linear expansion. Compared to the cubic-spline method, the linear-spline (LS) method can find turning locations of w$_{de}$ more accurately and reduce the errors due to less the number of bins. The LS method is also nearly model-independent, like the piecewise constant and cubic-spline method. Replacing the linear expansion by CPL parametrization in each bin, we have reached the almost same results. For the current status of observational data, LS method may be more suitable to study w$_{de}$ than the piecewise constant and the cubic spline method. If DE is dynamical or even oscillating, by using the LS method it should be more possible to find deviations from the cosmological constant, at the turning points the deviation from − 1 should be more explicit. If DE is just the cosmological constant, it seems more confident if the best-fitted linear expansions construct an w = − 1 line, while the oscillation of w$_{de}$ around w = − 1 could disappear by averaging with the piecewise constant method. Compared to the piecewise constant case, the only price we pay is that there is one more parameter in the LS method if the number of bins is the same in two cases. Compared to the cubic spline method, the form of w$_{de}$ ( z ) in each bin only depends on values of w$_{de}$ at two boundaries, thus the parameters in w$_{de}$ ( z ) will not be heavily correlated. Furthermore, the cubic-spline method seems not suitable for finding the turning points of w$_{de}$ . In all, the LS method could reconstruct w$_{de}$ explicitly by using the least number of bins, and errors of the parameters from observational data will be small, compared to the case with more bins. The paper is organized as follows. In section II we introduce in detail the method we will use and construct corresponding cosmological models. In section III, we show how to fit our model with 397 Constitution SnIa sample [18], BAO data from SDSS DR7 [19], CMB datapoints ( R, l$_{a}$, z$_{∗}$ ) from WMAP5 [20] and 12 Hubble evolution data [21, 22]. The fitting 3