  By starting from the non-standard quantum deformation of the sl(2,R) algebra,
a new quantum deformation for the real Lie algebra so(2,2) is constructed by
imposing the former to be a Hopf subalgebra of the latter. The quantum so(2,2)
algebra so obtained is realized as a quantum conformal algebra of the (1+1)
Minkowskian spacetime. This Hopf algebra is shown to be the symmetry algebra of
a time discretization of the (1+1) wave equation and its contraction gives rise
to a new $(2+1)$ quantum Poincar\'e algebra.
