  The analysis of the terminating bands has been performed in the relativistic
mean field framework. It was shown that nuclear magnetism provides an
additional binding to the energies of the specific configuration and this
additional binding increases with spin and has its {\it maximum} exactly at the
terminating state. This suggests that the terminating states can be an
interesting probe of the time-odd mean fields {\it provided that other effects
can be reliably isolated.} Unfortunately, a reliable isolation of these effects
is not that simple: many terms of the density functional theories contribute
into the energies of the terminating states and the deficiencies in the
description of those terms affect the result. The recent suggestion
\cite{ZSW.05} that the relative energies of the terminating states in the $N
\neq Z, A\sim 44$ mass region given by $\Delta E$ {\it provide unique and
reliable constraints on time-odd mean fields and the strength of spin-orbit
interaction} in density functional theories has been reanalyzed. The current
investigation shows that the $\Delta E$ value is affected also by the relative
placement of the states with different orbital angular momentum ${\it l}$,
namely, the placement of the $d$ (${\it l}=2$) and $f$ (${\it l}=3$) states.
This indicates the dependence of the $\Delta E$ value on the properties of the
central potential.
