Due to their unique manipulation capabilities, continuum robots find applications in a variety of different areas, such as medical technology or maintenance and repair. When working with continuum robots, it is often necessary to bend the structure according to complex shapes. This is commonly achieved by arranging several individual modules in series. In this paper, a novel continuum robot concept is presented based on a serial arrangement of SMA (Shape Memory Alloy) wires actuated modules. The key advantage of the described modular continuum robot is the number of connection wires required to control the SMA wires, which is also independent of the number of modules. This feature makes it possible to virtually connect a very large number of serial modules, thus enabling to design continuum robots with arbitrary complexity. After outlining the concept, the mechanical and electrical components required to build one module of such an SMA driven continuum robot are introduced.