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Many e-health projects and innovations are not established based on robust system requirements engineering phase. In order to ensure the success delivery of e-health services to stakeholders, all characteristics of e-health systems and applications must be understood in terms of technological perspectives as well as the all system requirements. Thus, this paper aims to introduce the Goal-Oriented Requirements Extraction Approach (GOREA). It is an elicitation approach that uses, specifically, healthcare business goals to derive the requirements of e-health system to be developed. It consists of two major phases: (1) modelling e-health business requirements phase; and (2) modelling e-health Information Technology (IT) and systems requirements phase. The modelling e-health business requirements phase is divided into two main stages: (1) model e-health business strategy stage; and (2) model e-health business environment stage. The modelling e-health IT and systems requirements phase illustrates the process of obtaining requirements of e-health system from the organizational goals that are determined in the previous phase. It consists of four main steps that deals with business goals of e-health system: (1) modelling e-health business process (BP) step; (2) modelling e-health business goals step; (3) analyzing e-health business goals step; and (4) eliciting e-health system requirements step. A case study based on the basic operations and services in hospital emergency unit for checking patient against COVID-19 virus and taking its diagnostic testing has been set and used to examine the validity of the proposed approach by achieving the conformance of the developed system to the business goals. The results indicate that: (1) the proposed GOREA has a positive influence on the system implementation according to e-health business expectations; and (2) it can successfully fulfil the need of e-health business in order to save the citizens life by checking them against COVID-19 virus.