  We show that a family of isolated complex hypersurface singularities with
constant Milnor number may fail, in the strongest sense, to have constant
bi-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 surface
germs; we show the germ $(X_0, 0)$ is not bi-Lipschitz homeomorphic with
respect to the inner metric to the germ $(X_t,0)$ for $t\ne 0$.
