  In this paper, we propose a finite Toda lattice of CKP type (C-Toda) together
with a Lax pair. Our motivation is based on the fact that the Camassa-Holm (CH)
peakon dynamical system and the finite Toda lattice may be regarded as opposite
flows in some sense. As an intriguing analogue to the CH equation, the
Degasperis-Procesi (DP) equation also supports the presence of peakon
solutions. Noticing that the peakon solution to the DP equation is expressed in
terms of bimoment determinants related to the Cauchy kernel, we impose opposite
time evolution on the moments and derive the corresponding bilinear equation.
The corresponding quartic representation is shown to be a continuum limit of a
discrete CKP equation, due to which we call the obtained equation finite Toda
lattice of CKP type. Then, a nonlinear version of the C-Toda lattice together
with a Lax pair is derived. As a result, it is shown that the DP peakon lattice
and the finite C-Toda lattice form opposite flows under certain transformation.
