  Based on general considerations such as $R$-operation and Slavnov-Taylor
identity we show that the effective action, being understood as Legendre
transform of the logarithm of the path integral, possesses particular structure
in ${\cal N} =4$ supersymmetric Yang--Mills theory for kernels of the effective
action expressed in terms of the dressed effective fields. These dressed
effective fields have been introduced in our previous papers as actual
variables of the effective action. The concept of dressed effective fields
naturally appears in the framework of solution to Slavnov-Taylor identity. The
particularity of the structure is the independence of these kernels on the
ultraviolet regularization scale $\Lambda.$ These kernels are functions of
mutual spacetime distances and of the gauge coupling. The fact that $\beta$
function in this theory is zero is used significantly.

High Energy Physics - Theory