In this paper, we prove that the binomial operator is a Hausdorff operator of the Euler type and consequently, the binomial matrix domain associated with this operator is nothing new except an Euler sequence space. Therefore, all the results of published papers on the binomial sequence spaces like [4], can be extracted easily from [1] and the relation between the binomial and Euler operators that we introduce. Moreover, we compute the norm and the lower bound of the binomial operator on some sequence spaces.