  We study the frustration properties of the Ising model on several decorated
lattices with arbitrary numbers of decorating spins on all bonds of the lattice
within an exact analytical approach based on the Kramers--Wannier
transfer-matrix technique. The existence of magnetic frustrations in such
situations and their influence on the behavior of the thermodynamic functions
of systems is shown. The most important result of our study is related to the
description of the possible coexistence of frustrations and long-range magnetic
order in partially ordered spin systems.
