In the recent years, Higher-order Side Channel attacks have been widely investigated. In particular, 2nd-order DPA have been improved and successfully applied to break several masked implementations. In this context, the development of sound and practical countermeasures against attacks of arbitrary xed order d is of crucial interest. Surprisingly, while many studies have been dedicated to the attacks, only a very few methods have been published that claim to provide security against dth-order side channel attacks whatever the order d. Among them, the one proposed by Courtois and Goubin at ICISC 2005 was especially interesting due to its great eciency. In this paper we show that the method is however awed and we exhibit several higher-order attacks that can defeat the countermeasure for any value of d.