Since the introduction of augmented Dickey-Fuller unit root tests, many new types of unit root tests have been developed. Developments in nonlinear unit root tests occurred to overcome poor performance of standard linear unit root tests for nonlinear processes. Venetis et al. (2009) developed a unit root test for the k-ESTAR(p) model where k is the number of equilibrium levels and p is the order of autoregressive terms. Their approach may cause singularity problem because some of the regressors might be collinear. To overcome the problem, they move collinear regressors into the error term. This paper extends the work of Venetis et al. (2009). Using a new approach given in this paper, the singularity problem can be avoided without worrying the issue of collinearity. For some cases, simulation results show that our approach is better than other unit root tests.