  Variational principles for magnetohydrodynamics were introduced by previous
authors both in Lagrangian and Eulerian form. In a previous work Yahalom &
Lynden-Bell introduced a simpler Eulerian variational principles from which all
the relevant equations of magnetohydrodynamics can be derived. The variational
principle was given in terms of six independent functions for non-stationary
flows and three independent functions for stationary flows. This is less then
the seven variables which appear in the standard equations of
magnetohydrodynamics which are the magnetic field $\vec B$ the velocity field
$\vec v$ and the density $\rho$. In this work I will improve on the previous
results showing that non-stationary magnetohydrodynamics should be described by
four functions .
