Two gapped quantum ground states in the same phase are connected by an adiabatic evolution which gives rise to a local unitary transformation that maps between the states. Therefore, local unitary transformations define an equivalence relation among states in the same universality class of a gapped quantum phase, hence with the same topological order. Based on the tensor product representation of quantum ground states, we give an explicit construction of a specific local unitary transformation which performs wave function renormalization and flows a wavefunction to a simpler form within the same equivalence/universality class. The fixed point under this renormalization scheme gives a classification of topological order. First, we discuss the situation in 1D spin chains and show that there is no topological order in 1D, i.e. every state can be mapped to product states with local unitary transformations. Further, we classify all possible phases in 1D spin chains when certain symmetry is required for the system. Next, we will show how such a renormalization procedure can be carried out in 2D and demonstrate some examples where it can be used to identify phase transition points, for both topological and symmetry breaking phases.