The paper provides the estimate \({1\over 2p}\leq \left| y \right| \leq {1 \over 2}\) for a root \(y\) of a polynomial of degree \(p-1\) which appears from the construction of Daubechies orthogonal mother wavelet with two channel filter bank. For previous works on this topic see [N. M. Temme, Asymptotics and numerics of zeros of polynomials that are related to Daubechies wavelets. Appl. Comput. Harmon. Anal. 4, No. 4, 414–428 (1997; Zbl 0903.42016)] and [G. Strang, Wavelets from filter banks. Ainsworth, M. (ed.) et al., Wavelets, multilevel methods and elliptic PDEs. 7th EPSRC numerical analysis summer school, University of Leicester, Leicester, GB, July 8–19, 1996. Oxford: Clarendon Press. Numerical Mathematics and Scientific Computation. 161–211 (1997; Zbl 0888.65140)].