Summary: The present paper proves that if \(f(x)\in C_{[0,1]}\), changes its sign exactly \(l\) times at \(0< y_1< y_2<\cdots< y_t<1\) in \((0,1)\), then there exists a \(p_n(x)\in\Pi_n(+)\), such that \[ \biggl|f(x)- \frac{\rho(x)}{p_n(x)}\biggr|\leq C\omega_\varphi(f,n^{-1/2}), \] where \(\rho(x)\) is defined by \[ \rho(x)=\begin{cases} \prod_{i=1}^l(x-y_i), &\text{if }f(x)\geq 0\text{ for }x\in(y_l,1),\\ -\prod_{i=1}^l(x-y_i),&\text{if }f(x)<0\text{ for }x\in(y_l,1), \end{cases} \] which improves and generalizes the results of \textit{M. Liang, D. Zhou, J. Liu} and \textit{J. Ma} [J. Shanghai Jiaotong Univ. (Chin. Ed.) 39, No. 5, 769--773, 781 (2005; Zbl 1080.74540)].