An agent-based system is a complex software system with functional and non-functional requirements. Non-functional requirements (NFRs) are crucial software requirements that have been specified early in the software development process while eliciting the functional requirements (FRs) in agent oriented software development. Some of the functional and non-functional attributes are of a crosscutting nature i.e. it is difficult to represent clearly how an attribute may effect several other requirements simultaneously. In our previous work, we presented a methodology for open and adaptive system to provide a clear separation between requirement gathering and analysis phases. In this paper, we propose a new analysis method based on the methodology proposed by us in our previous work. This new analysis methodology splits the analysis phase into the System User centric Analysis and the System centric Analysis phases. This refinement is achieved by identification and separation of all requirements into three types of requirements i.e. Functional, Non-Functional and Crosscutting requirements.