  We present a new type of integrable one-dimensional many-body systems called
a one-parameter Calogero-Moser (CM) system. In the discrete level, the Lax
pairs with a parameter are introduced and, of course, the discrete-time
equations of motion are obtained as well as their corresponding discrete-time
Lagrangian. The integrability feature of this new system can be captured
through the discrete Lagrangian closure relation by employing a connection with
the temporal Lax matrices of the discrete-time Ruijsenaars-Schneider (RS)
system, exact solution, and the existence of the classical r-matrix. Under the
appropriate limit on the parameter, which in this case is approaching zero, the
standard CM system is retrieved both discrete-time and continuous-time.
