The construction energy matrix and characters of the matrixs are introduced when different electron spin exchange in the sites of Heisenberg chain in one dimension. There are three situations that the sites of Heisenberg chain are filled with single electron only, two electrons only, or single and two electrons at the same time. The exchanges of electron spin of the nearest neighbor site are classified into two sorts. The first sort is the exchange of the nearest electron spin. The second sort is the exchange between the left and the left (or the right and the right) electron spin. The Hamiltonian operator of system of Heisenberg chain acts on the complete basis vectors produced with permutation group to form energy matrix. The calculating results are the following. (1)When the sites are filled with single, two electrons and them at the same time, the matrixs of [4,2] are different except for the sites filled with symmetrica election spin. (2)When the sites are filled with two electrons, the matrixs of [4,2] formed in the second sort are different from that in the first sort except for the sites filled with symmetrica election spin. The same Hamiltonian operator acts on the same complete basis vectors to produce same or different matrixs contrast the exchange between the left and the left neighbor electron spin to the exchange between the right and the right neighbor electron spin. Finally, the rules of the matrixs and their studying significance are showed.