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We find a two-parameter family of ordinary differential systems in dimensionfive with the affine Weyl group symmetry of type $D_3^{(2)}$. We show itssymmetry and holomorphy conditions. This is the second example which gavehigher order Painlev\'e type systems of type $D_{3}^{(2)}$. By obtaining itsfirst integrals of polynomial type, we can obtain a two-parameter family ofcoupled Hamiltonian systems in dimension four with the polynomial Hamiltonian.

Coupled Hamiltonian systems with extended affine Weyl group symmetry of type $D_3^{(2)}$