A simple method is proposed for constructing fourth-degree cubature formulae over general product regions with no symmetric assumptions. The cubatureformulae that are constructed contain at most n2 + 7n + 3 nodes and they are likelythe first kind of fourth-degree cubature formulae with roughly n2 nodes for nonsymmetric integrations. Moreover, two special cases are given to reduce the numberof nodes further. A theoretical upper bound for minimal number of cubature nodesis also obtained.
