  We study tree-unitarity and renormalizability in Lifshitz-scaling theory,
which is characterized by an anisotropic scaling between the spacial and time
directions. Due to the lack of the Lorentz symmetry, the conditions for both
unitarity and renormalizability are modified from those in relativistic
theories. For renormalizability, the conventional discussion of the power
counting conditions has to be extended. Because of the dependence of $S$-matrix
elements on the reference frame, unitarity requires stronger conditions than
those in relativistic cases. We show that the conditions for unitarity and
renormalizabilty are identical as in relativistic theories. We discuss the
importance of symmetries for a theory to be renormalizable.
