Safety-critical system development requires a clear description of the activities performed and their work products. This aids the developers in performing the correct activities, and it is also required by several modern safety standards. It is therefore important that a well-specified development process is used. There are existing, well-established system life cycles that provide a high-level description of developing a safetycritical system. The V-model is the most-widely applied. However, these do not specify the detailed steps that must be performed, nor do they typically specify in detail the work products that should be produced. In this paper, we present a detailed process for performing the design stages of the system life cycle. We have extended the existing Object-Oriented Systems Engineering Method to clearly specify its activities and roles, and added the necessary steps and work products for the safety-related aspects of development.