Beams passing through a solenoid fringe field experience x-y coupling andchange of their eigen-emittances. As reported previously (C.~Xiao et al., Phys.Rev. ST Accel. Beams 044201, {\bf 16} 2013) constant settings of a subsequentdecoupling section can be found such that variation of the fringe fieldstrength will not change the Twiss parameters $\beta$ and $\alpha$ in bothtransverse planes at the exit of the decoupling section. For time being thisfeature was understood for a generic beam line but not to the generality towhich it is observed. This report is on explanation of the convenientdecoupling of fringe-coupled beams by any beam line that provides decoupling.For better coherence this report includes recapitulation of previous works.
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