In the past, much research work has focused on designing optimal multi-attribute file systems for partial match queries (PMQs). However, prior works on designing a multi-attribute file system for orthogonal range queries (ORQs) were usually based on heuristic methods. In this paper, we particularly concentrate on designing the optimal two-attribute Cartesian product file (CPF) for ORQs. We present two important properties of the two-attribute CPF partition form for ORQs. The first property is that the closer the number of partitions of each domain is to the other, the better the performance the CPF will achieve. By this property, we can adjust the number of partitions of each domain of a partition from to obtain a better partition form. The second property is that the partition form with the larger number of partitions being assigned to the smaller domain will perform better than will the other partition form. By this property, we can change the order of numbers in a partition form to obtain better performance. Furthermore, we also show that the problem of designing the optimal two-attribute CPF for ORQs is partially related to the problem of finding a minimal 2-tuple with positive order. Based on these properties, an algorithm to find the optimal two-attribute CPF for ORQs is presented.