This paper presents a European Master programme on global software engineering (SE), being put forward by four leading institutions from Sweden, UK, Netherlands and Italy. The Global SE European Master (GSEEM) programme aims to provide students with an excellence in SE based on sound theoretical foundations and practical experience, as well as prepare them to participate in global development of complex and large software systems. GSEEM has been designed with three noteworthy aspects: 1) Three specialization profiles in which the consortium excels: Software Architecting, Real-time Embedded Systems Engineering, and Web Systems and Services Engineering. 2) Two market-driven routes: "professional" to work as professionals, and "scientific" to continue the education towards research degrees. 3) An innovative concept of "shared modules", delivered together by multiple institutions. Four types of shared modules are foreseen: "parallel" twin modules which run remotely between universities, "shifted" modules which teach SE concepts incrementally with shifts in study locations and timeline ,"complementary" modules in which complementary SE concepts are taught in parallel through shared projects, and "common" modules which share the presentations and the project. The profiles realize "integrated knowledge" by complementing partial knowledge available at partner institutions. The paper explains how GSEEM achieves the objectives of educating global software engineers.