\begin{block}{A (coarse) two steps approach} \begin{enumerate} \item Sufficient conditions to retrieve Boolean maps whose graphs are strongly connected are given \item Further filter those whose Markov matrix is doubly stochastic \end{enumerate} \end{block} \begin{block}{Drawback} Delaying the second requirement to a final step whereas this is a necessary condition \end{block} \begin{block}{Content of this work} A completely new approach to generate Boolean functions, whose Markov matrix is doubly stochastic and whose graph of iterations is strongly connected (denoted as DSSC Matrix) \end{block}