  We investigate a new class of improved relativistic fermion action on the
lattice with a criterion to give excellent energy-momentum dispersion relation
as well as to be consistent with tree-level $O\left(a^{2}\right)$-improvement.
Main application in mind is that for heavy quark for which $ma\simeq O(0.5)$.
We present tree-level results and a scaling study on quenched lattices.
