  By differentiating the dressed quark propagator with respect to a variable
background field, the linear response of the dressed quark propagator in the
presence of the background field can be obtained. From this general method,
using the vector background field as an illustration, we derive a general
formula for the four-quark condensate $<{\tilde 0}|:{\bar q}(0)\gamma_\mu
q(0){\bar q}(0)\gamma_\mu q(0):|{\tilde 0}>$. This formula contains the
corresponding fully dressed vector vertex and it is shown that factorization
for $<{\tilde 0}|:{\bar q}(0)\gamma_\mu q(0){\bar q}(0)\gamma_\mu q(0):|
{\tilde 0}>$ holds only when the dressed vertex is taken to be the bare one.
This property also holds for all other type of four-quark condensate.
