  Usually we consider the symmetry of action as the symmetry of the theory,
however, in the Keplar problem the scaling symmetry existing in equa tion of
motion is not the ones for action. It changes the multiplicative c onstant of
action and the time boundary. In such a case that the scale tran sformation
does not leave the action invariant but keeping the equation inva riant, the
following statement is proved. The time integration of Lagrangian is explicitly
performed and the action ca n be expressed by the difference of formal
(non-conserved) Noether charges a t time boundaries. In field theory the action
can be expressed by the bound ary integration of the formal Noether current.
