Abstract: The lossless constraint conditions of the non-reciprocal passive networks are studied in this paper. It is shown that the impedance matrix [Z] of a non-reciprocal lossless network has the real part, but it is compatible with the law of conservation of energy. In the non-reciprocal case, the positive resistances of the impedance matrix do not represent the. loss of the network, and the negative resistances do not represent the active gain. In addition, the transmission matrix [A] has the characteristic of |det[/l]|=l, which is called as the quasi- reciprocity. The realistic examples are given hi this paper.