  In the equation of motion approach to the two-time Green's functions,
conventional Tyablikov-type truncation of the chain of equations is rather
arbitrary and apt to violate the analytical structure of Green's functions.
Here, we propose a practical way to truncate the equations of motion using
operator projection. The partial projection approximation is introduced to
evaluate the Liouville matrix. It guarantees the causality of Green's
functions, fulfills the time translation invariance and the particle-hole
symmetry, and is easy to implement in a computer. To benchmark this method, we
study the Anderson impurity model using the operator basis at the level of
Lacroix approximation. Improvement over conventional Lacroix approximation is
observed. The distribution of Kondo screening in the energy space is studied
using this method.
