As business collaboration involves multiple business processes from different participating organisations, it becomes a challenging issue to manage the complex correspondence between instances of these business processes. Yet very limited support has been provided by inter-organisational workflow research. In this paper, we develop a formal method to specify instance correspondence based on a novel correspondence Petri net model. In this method, cardinality parameters are defined to represent cardinality relationships between collaborating business processes at build time, while correlation structures are designed to characterise correspondence between collaborating business process instances at run time. Corresponding algorithms are also developed to generate the correspondence Petri nets for collaborative business processes, and to trace instance correlation on the fly using the generated Petri nets.