  Recently it has been advocated [1] that for describing nature within the
minimal symmetry requirement, certain subgroups of Lorentz group may play a
fundamental role. One such group is E(2) which induces a Lie algebraic
Non-Commutative spacetime [4] where translation invariance is not fully
maintained. We have constructed a consistent structure of Non-commutative phase
space for this system and furthermore we have studied an appropriate point
particle action on it. Interestingly, the Einstein dispersion relation
$p^2=m^2$ remains intact. The model is constructed by exploiting a dual
canonical phase space following the scheme developed by us earlier [8].
