Let (b$_{i,j}$) be a bounded matrix on extit{ l}$^{2}$, $Bbb T={zinBbb C:|z|=1}$, and A be a bounded matrix on L$^{ 2}(mathbb{T)}$ satisfying the conditions 1.$langle Az^{2j},z^{2i} angle =sigma ^{-1}b_{ij}+|alpha |^{2}sigma ^{-1}langle Az^{j},z^{i} angle $; 2.$langle Az^{2j},z^{2i-1} angle =-alpha sigma ^{-1}b_{ij}+alpha sigma ^{-1}langle Az^{j},z^{i} angle $; 3.$langle Az^{2j-1},z^{2i} angle =-overline{alpha }sigma ^{-1}b_{ij}+overline{alpha }sigma ^{-1}langle Az^{j},z^{i} angle$; 4.$langle Az^{2j-1},z^{2i-1} angle =|alpha |^{2}sigma ^{-1}b_{ij}+sigma ^{-1}langle Az^{j},z^{i} angle $ hspace{-0.76cm} for all $i,jin mathbb{Z}$, where $sigma =1+|alpha |^{2},,alpha in mathbb{C},alpha eq0$. The above conditions evidently suggests that there is a "dyadic" relation in the entries of $A$. Here in the following picture illustrates how each $ij-$th entry of $A$ generates the 2 by 2 block in $A$ with entries ${a_{2i 2j}, a_{2i-1 2j}, a_{2i 2j-1}, a_{2i-1 2j-1}}.$ vspace{-0.3cm} egin{figure}[hp] egin{center} includegraphics[scale=0.42]{cubic.pdf} end{center} vspace{-0.8cm}caption{The dyadic recurrent form} end{figure} It has been shown [2] that $displaystyle A=sum_{n=0}^{infty }S^{n}BS^{ast n}$, where $Sz^i=sigma ^{-1/2}(overline{alpha }z^{2i}+z^{2i-1})$ and $$B=sumlimits_{i=-infty}^infty sumlimits_{j=-infty}^infty b_{ij}(u_{i}otimes u_{j}), u_{i}(z)=sigma ^{-1/2}z^{2i-1}(alpha -z).$$ In this paper, we shall use the above relations to compute $langle a_{i,j} angle $ explicitly. ewline Key words: shift operator, bounded matrix, dyadic recurrent formula, slant Toeplitz operator, separable Hilbert space 2.$langle Az^{2j},z^{2i-1} angle =-alpha sigma ^{-1}b_{ij}+alpha sigma ^{-1}langle Az^{j},z^{i} angle $ 3.$langle Az^{2j-1},z^{2i} angle =-overline{alpha }sigma ^{-1}b_{ij}+overline{alpha }sigma ^{-1}langle Az^{j},z^{i} angle $ 4.$langle Az^{2j-1},z^{2i-1} angle =|alpha |^{2}sigma ^{-1}b_{ij}+sigma ^{-1}langle Az^{j},z^{i} angle $ for all $i,jin mathbb{Z}$, where $sigma =1+|alpha |^{2},,alpha in mathbb{C},alpha eq0$ egin{figure}[hp] egin{center} includegraphics[scale=0.42]{cubic.pdf} end{center} caption{The dyadic recurrent form} end{figure} Since it has been shown [2] that $displaystyle A=sum_{n=0}^{infty }S^{n}BS^{ast n}$, where $ Sz^i=sigma ^{-1/2}(overline{alpha }z^{2i}+z^{2i-1})$ $ B=sum sum b_{ij}(u_{i}otimes u_{j})$ ;;; which $u_{i}(z)=sigma ^{-1/2}z^{2i-1}(alpha -z)$ Then we can use it to compute $langle Az^{j},z^{i} angle $ explicity if A satisfies the previous condition. ewline Key words: shift operator, bounded matrix, dyadic recurrent formula, slant Toeplitz operator, separable Hilbert space