  We propose a Hamiltonian formalism for $N$ periodic dressing chain with the
even number $N$. The formalism is based on Dirac reduction applied to the $N+1$
periodic dressing chain with the odd number $N+1$ for which the Hamiltonian
formalism is well known. The Hamilton dressing chain equations in the $N$ even
case depend explicitly on a pair of conjugated Dirac constraints and are
equivalent to $A^{(1)}_{N-1}$ invariant symmetric Painlev\'e equations.
