The linearized stability of stationary solutions for surface diffusion is studied. We consider hypersurfaces that lie inside a fixed domain, touch its boundary with a right angle and fulfill a no-flux condition. We formulate the geometric evolution law as a partial differential equation with the help of a parametrization from Vogel [Vog00], which takes care of a possible curved boundary. For the linearized stability analysis we identify as in the work of Garcke, Ito and Kohsaka [GIK05] the problem as an H