  We study a generalization of Swendsen-Wang algorithm suited for Potts models
with next-next-neighborhood interactions. Using the embedding technique
proposed by Wolff we test it on the Symanzik improved bidimensional non-linear
$\sigma$ model. For some long range observables we find a little slowing down
exponent ($z \simeq 0.3$) that we interpret as an effect of the partial
frustration of the induced spin model.
