  A new symmetric Hamiltonian constraint operator is proposed for loop quantum
gravity, which is well defined in the Hilbert space of diffeomorphism invariant
states up to non-planar vertices with valence higher than three. It inherits
the advantage of the original regularization method, so that its regulated
version in the kinematical Hilbert space is diffeomorphism covariant and
creates new vertices to the spin networks. The quantum algebra of this
Hamiltonian is anomaly-free on shell, and there is less ambiguity in its
construction in comparison with the original method. The regularization
procedure for this Hamiltonian constraint operator can also be applied to the
symmetric model of loop quantum cosmology, which leads to a new quantum
dynamics of the cosmological model.
