The ability to control boundary behaviors is critical for the subdivision surface to become a useful representation in computer aided geometric design. Previous methods achieve boundary control by extending the boundary vertices of the control mesh, or by applying different subdivision rules to the boundary edges and vertices. This paper presents an open uniform quadratic subdivision scheme derived from the subdivision of open uniform B-spline surfaces. For meshes with 4-sided boundary and corner faces, the cross-tangent along the boundary curves can also be derived. The proposed scheme leads to a straightforward boundary control that enables two subdivision surfaces to be joined with C0 and C1-continuity.