  A self-consistent theory for two-particle fluctuations with renormalized
irreducible vertices is proposed. Using the Parquet formalism, we construct the
fully antisymmetric full vertex in terms of the two-particle fluctuations in
the charge, the spin and the particle-particle channels on an equal footing to
satisfy the Pauli principle. The fluctuations are determined self-consistently,
which are reflected into the one-particle self-energy via the Schwinger-Dyson
equation. We demonstrate the application of the present theory to the impurity
Anderson model and the Hubbard model on a square lattice mainly for the
particle-hole symmetric case. In both models the vertex renormalization in the
spin channel eliminates magnetic instabilities of mean-field theory to ensure
the Mermin-Wagner theorem. The present theory gives the same critical exponents
of the self-consistent renormalization theory in the quantum critical region.
