In this paper we focus on a type of Unimodular polynomial pair used for digital systems and present some new properties of them which lead us to estimation of their autocorrelation coefficients and the moments of a Rudin-Shapiro polynomial product. Some new results on the Rudin-shapiro sequences will be presented in the last section. Main Facts: For positive integers M and n with $M;<;2^n$ - 1, consider the $2^n$ - M numbers ${epsilon}_k$ ($M;{leq};k;{leq};2^n$ - 1) which form a collection of Rudin-Shapiro coefficients. We verify that $|{sum}_{k=M}^{2^{n-1}};{{epsilon}_k}e^{ikt}|$ is dominated by $(2+sqrt{2});sqrt {2^n-M}-{sqrt{2}}$.