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We show that a family of isolated complex hypersurface singularities withconstant Milnor number may fail, in the strongest sense, to have constantbi-Lipschitz type. Our example is the Briac con--Speder family$X_t:=\{(x,y,z)\in\C^3 | x^5+z^{15}+y^7z+txy^6=0 \}$ of normal complex surfacegerms; we show the germ $(X_0, 0)$ is not bi-Lipschitz homeomorphic withrespect to the inner metric to the germ $(X_t,0)$ for $t\ne 0$.

mu-constancy does not imply constant bi-Lipschitz type