  Our main contribution here is the discovery of a new family of standard Young
tableaux $ {\cal T}^k_n$ which are in bijection with the family ${\cal
D}_{m,n}$ of Rational Dyck paths for $m=k\times n\pm 1$ (the so called "Fuss"
case). Using this family we give a new proof of the invertibility of the sweep
map in the Fuss case by means of a very simple explicit algorithm. This new
algorithm has running time $O(m+n)$. It is independent of the Thomas-William
algorithm.
