The deformation of a continuous facesheet DM with discrete push-pull actuators in the thin plate approximation is described by the differential equation. Analysis of the equation shows that to achieve a high quality correction of low-order aberrations, deformable mirrors should have some actuators positioned outside the correction aperture. By finite element analysis, the correcting abilities of defocus, astig and coma are compared. A novel design of 9 actuators positioned on the edge of aperture and mirror is proposed and optimized. The analysis results show that the new design improves the correcting abilities, especially for coma which is hard to correct. Finally the wavefront correction and modal correction methods are compared.