A new numerical method is formulated which belongs in discrete ones rather than mode methods of unsteady subsonic lifting surfaces. This may be said a final form (revision and extension) of the DSM (Doublet Strip Method). After integrating spanwise first the kernel function across a narrow chordwise strip, there appear just similar singular terms as in the DLM-C for two-dimensional airfoils. Thus Mangler's principal value can be avoided. The following chordwise quadrature may be carried out efficiently as in the DLM-C developed by our laboratory in past. This new method is designated as BIS (Box-in-Strip) method. Authors' basic thought is stated concerning about the reason for being of efficient linearized lifting surface methods, especially at high reduced frequencies and high subsonic Mach numbers. It is often not wellunderstood in our country. It is noted that results obtained through lifting surface methods may have significant influences into some other numerical schemes, such as Surface Singularity Method.