The exact bounds of Bernstein and Meyer-König and Zelley basis functions have been determined in [X. Zeng, J. Math. Anal. Appl. 219, No. 2, 364-376 (1998; Zbl 0909.41015)]. In this note the exact bound of basis function \(M_{\alpha,k}(x)={\alpha+k-1\choose k}x^k(1-x)^{\alpha}\) was obtained. That is \(x^{\frac{1}{2}}M_{\alpha,k}(x)<c_j\alpha^{-\frac{1}{2}}\), where \(c_j=((j+\frac{1}{2})^{j+\frac{1}{2}}/j!)e^{-(j+\frac{1}{2})}\). Some multivariate basis function were also considered.