As a standard modeling language for definition of business processes and services, BPMN is used both within the organizations as well as for co-creation of joint services to run among the networked organizations. However, introducing certain constructs, such as OR-join and Complex-join in BPMN Process Diagrams (BPDs) can lead to execution problems, due to ambiguities inherent in these constructs in relation to their execution semantics. Although these constructs are often used to represent the real-world behaviors, none of the existing approaches applied by the BP management systems are practically tuned to disambiguate and support their proper execution. Rooted in workflow patterns concept, we first introduce a set of algorithms to automate the identification of ambiguous patterns (i.e., workflow patterns that include OR-join constructs). Then, we introduce a set of equivalent unambiguous BP fragments that can substitute those ambiguous patterns. To this end, we have conceptualized the identification of three OR-join ambiguous patterns by applying the RPST technique, represent a set of unambiguous solutions for their substitution, and implemented our method as the proof of concept for our approach.