As is known, the minimum magnetic energy state for a frozen plasma, subject to the infinite topological constraints, corresponds to a nonlinear force-free field. The magnetic flux invariance in ideal magnetohydrodynamics is possible in important astrophysical applications. We develop a method for explicitly obtaining a minimum energy state starting from an arbitrary initial state. This method does not require the explicit use of the invariance of the differential magnetic helicities. It is particularly useful when the minimum magnetic energy state for the given topological structure is unique. We show examples of the application of the method for this kind of system.