  In this paper, we performed the comprehensive studies of frustration
properties in the Ising model on a decorated square lattice in the framework of
an exact analytical approach based on the Kramers--Wannier transfer matrix
method. The assigned challenge consisted in finding rigorous formulas for
residual entropies of all possible frustrations without exception and
elucidating the influence of frustrations on the behavior of the thermodynamic
functions of the system under discussion. The accomplished results turned out
to be very rich and intricate, especially in comparison with the original
undecorated square lattice, in which frustration properties are completely
absent. Such an abundance of properties is due to the multiparametric problem
of decorated lattice with four exchange interactions $J_{x}$, $J_{y}$, $J_{dx}$
and $J_{dy}$ taking on arbitrary continuous values and different signs:
positive (ferromagnetic) and negative (antiferromagnetic), as well as with two
discrete variables $d_{x}$ and $d_{y}$ (multiplicities of decorating spins in
both lattice directions), corresponding to infinite natural series of numbers.
