  We study the q-deformation of the bi-local system, two particle system,
bounded by a relativistic harmonic oscillator type of potential from both
points of view of mass spectra and the behavior of scattering amplitudes. In
particular, we try to formulate the deformation so that $P^2$, the square of
center of mass momenta, enters into the deformation parameters of relative
coordinates. As a result, the wave equation of the bi-local system becomes
non-linear one with respect to $P^2$; then, the propagator of the bi-local
system suffers significant change so as to get a convergent self energy to
second order.
