Let MnMn be the set of all nn-by-nn real matrices, and let RnRn be the set of all nn-by-11 real (column) vectors. An nn-by-nn matrix R=[rij]R=[rij] with nonnegative entries is called row stochastic, if ∑ nk=1rik∑ k=1nrik is equal to 1 for all ii, (1≤ i≤ n)(1≤ i≤ n). In fact, Re=eRe=e, where e=(1, … , 1)t∈ Rne=(1, … , 1)t∈ Rn. A matrix R∈ MnR∈ Mn is called integral row stochastic, if each row has exactly one nonzero entry, +1+1, and other entries are zero. In the present paper, we provide an algorithm for constructing integral row stochastic matrices, and also we show the relationship between this algorithm and majorization theory.