Wolff algorithm for anisotropic Ising model

Question

Is there way to simulate a 2D Ising model with anisotropic coupling parameter $J_{ij}$ and zero external field using Wolff algorithm?

Particularly, I am looking for when coupling parameter $J_{ij}=J_h$ for all horizontal bonds and $J_{ij}=J_v$ for all vertical bonds.

What I think

I think, while adding a spin into cluster, if the neighboring spin of cluster is same as spin in the cluster, then we include that spin in cluster with probability $1-e^{-beta J_v}$ if neighboring spin is below or above the cluster, or otherwise, if spin is at left-or-right of the cluster, then we include with probability $1-e^{-beta J_h}$. But this is just a hunch, not sure if this is right way.