  The alternative version of Hamiltonian formalism for higher-derivative
theories is proposed. As compared with the standard Ostrogradski approach it
has the following advantages: (i) the Lagrangian, when expressed in terms of
new variables yields proper equations of motion; no additional Lagrange
multipliers are necessary (ii) the Legendre transformation can be performed in
a straightforward way provided the Lagrangian is nonsingular in Ostrogradski
sense. The generalization to singular Lagrangians as well as field theory are
presented.
