For classical Hamiltonian with general form

we find a new convenient way to obtain its normal coordinates, namely, let

*H* be quantised and then employ the invariant eigen-operator (IEO) method (Fan

*et al*. 2004

*Phys. Lett.* A

**321** 75) to derive them. The general matrix equation, which relies on

*M* and

*L*, for obtaining the normal coordinates of

*H* is derived.