  The so called "New Massive Gravity" in $D=2+1$ consists of the
Einstein-Hilbert action (with minus sign) plus a quadratic term in curvatures
($K$-term). Here we perform the Kaluza-Klein dimensional reduction of the
linearized $K$-term to $D=1+1$. We end up with a fourth-order massive
electrodynamics in $D=1+1$ described by a rank-2 tensor. Remarkably, there
appears a local symmetry in $D=1+1$ which persists even after gauging away the
Stueckelberg fields of the dimensional reduction. It plays the role of a $U(1)$
gauge symmetry. Although of higher-order in derivatives, the new $2D$ massive
electrodynamics is ghost free, as we show here. It is shown, via master action,
to be dual to the Maxwell-Proca theory with a scalar Stueckelberg field.
