  A ghost-free metric formulation of the recently proposed covariant Galileon
model \cite{RPgal} which retains the internal shift symmetry has been
constructed. This presents a new result because the covariant Galileon models
introduced so far in the literature lacks the full Galileon symmetry. We
demonstrate that the same general procedure is applicable to all the Galileon
interaction terms and the resulting ghost-free Galileon action respecting
internal shift symmetry cannot predict the late time acceleration of the
universe. However, weakly breaking the shift symmetry in the covariant Galileon
Lagrangian, allows us to include an appropriate potential term which can
explain late time acceleration, in accordance with recent findings in the
literature.
