We investigate dynamical behavior of the equation of state of dark energy $w_{de}$ by employing the linear-spline method in the region of low redshifts from observational data (SnIa, BAO, CMB and 12 $H(z)$ data). The redshift is binned and $w_{de}$ is approximated by a linear expansion of redshift in each bin. We leave the divided points of redshift bins as free parameters of the model, the best-fitted values of divided points will represent the turning positions of $w_{de}$ where $w_{de}$ changes its evolving direction significantly (if there exist such turnings in our considered region). These turning points are natural divided points of redshift bins, and $w_{de}$ between two nearby divided points can be well approximated by a linear expansion of redshift. We find two turning points of $w_{de}$ in $zin(0,1.8)$ and one turning point in $zin (0,0.9)$, and $w_{de}(z)$ could be oscillating around $w=-1$. Moreover, we find that there is a $2sigma$ deviation of $w_{de}$ from -1 around $z=0.9$ in both correlated and uncorrelated estimates.
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