The concept of local stiffness associated with transverse local spin fluctuations is introduced and used to investigate the coupling between the magnetization of atomic planes in the ferromagnetic state of a metallic material. It is shown that the coupling strength in the surface region may differ significantly from that in the bulk, and the possibility of an antiferromagnetic alignment between surface and bulk magnetizations is pointed out. A comparison between calculated values of local and spin-wave stiffnesses is presented, and the stability of the ferromagnetic state against both short- and long-wavelength spin fluctuations is discussed.