Poynting vector in metamaterials

Poynting vector in a material with magnetic permeability $mu$ is defined as

$mathbf{S}=frac{1}{mu}(mathbf{E} times mathbf{B})$

In certain media $mu$ can be negative. In that case, $S$ will change sign. Does it mean that the wave propagation (in $vec k=vec E times vec B$ direction) and energy transfer (in $vec S$ direction) are happening in opposite directions? I think I’m mistaking something. Can anyone help?