An ongoing research has applied of calculus of variations to the portions of the deformation gradient multiplicative decomposition. This provides the stress equations of equilibrium and an internally balanced equation which is used to determine the decomposed portions of deformation gradient. To avoid the complexity of solving the internal balance tensorial equation, the internal balance equation is often expressed in the principal direction. However, this approach is allowed only if C=F^T F and C ̆=F ̆^T F ̆ are coaxial. This limits the previous work to use simple forms of constitutive models that grants the coaxiality of C and C ̆. These forms are based on some of the principal invariants of C ̆ and C ̂=F ̂^T F ̂ but not all of them. The novelty of this work is to demonstrate that tensors C and C ̆ are coaxial for a general form of constitutive model including all principal invariants of C ̆ and C ̂. This provides a simpler representation of internal balance equation and allows future use of recently developed linearization procedure for finite element analysis. A numerical verification is carried out using internally balanced constitutive model based on all principal invariants of C ̆ and C ̂ and it formulated in analogy to Blatz – Ko material model.