  We define a new model of interface roughening which has the property that the
minimum of interface height is conserved locally during the growth. This model
corresponds to the limit $q \to \infty$ of the q-color dimer
deposition-evaporation model introduced by us earlier [Hari Menon M K and Dhar
D 1995 J. Phys. A: Math. Gen. 28 6517]. We present numerical evidence from
Monte Carlo simulations and the exact diagonalization of the evolution operator
on finite rings that this model is not in the universality class of the
Kardar-Parisi-Zhang interface growth model. The dynamical exponent z in one
dimension is larger than 2, with $z \approx 2.5$. And there are logarithmic
corrections to the scaling of the gap with system size. Higher dimensional
generalization of the model is briefly discussed.
