Purification of non-maximally entangled two-atom states and three-atom states is investigated by means of entanglement swapping,which is generalized to non-maximally entangled multi-atom states'purification. It is found that the purification probabilities in all kinds of entangled atom states are the same,2|b|²,which is equal to twice modulus of the least coefficient of four coefficients in entangled atom states.