  We investigate generators of local transformations in the covariant canonical
formalism (CCF). The CCF treats space and time on an equal footing regarding
the differential forms as the basic variables. The conjugate forms $\pi_A$ are
defined as derivatives of the Lagrangian $d$-form $L(\psi^A, d\psi^A)$ with
respect to $d\psi^A$, namely $\pi_A := \partial L/\partial d\psi^A$, where
$\psi^A $ are $p$-form dynamical fields. The form-canonical equations are
derived from the form-Legendre transformation of the Lagrangian form
$H:=d\psi^A \wedge \pi_A - L$. We show that the Noether current form is the
generator of an infinitesimal transformation $\psi^A \to \psi^A + \delta
\psi^A$ if the transformation of the Lagrangian form is given by $\delta L=dl$
and $\delta \psi^A$ and $l$ depend on only $\psi^A$ and the parameters. As an
instance, we study the local gauge transformation for the gauge field and the
local Lorentz transformation for the second order formalism of gravity.
