Abstract: Lu and Sun（2000） first discussed the problem of constructing supersaturated design with more than two levels. A criterion, E（d²）, was proposed in the construction of supersturated design, and some E（d²）-optimal designs were obtained. In this paper, we use the criterion of Max（d²） in the construction of supersaturated design. A kind of method was discussed, some 3- and 4-level designs with prescribed Max（d²） are given.