electromagnetic radiation - Two possible directions of the B field in relation to the E field in radio waves. How induce the left-handed direction?

In vacuum the two field components of a radio wave are directed perpendicular on each over. $\mathbf{E}$, $\mathbf{B}$ and $\mathbf{k}$ form a right hand system ($\mathbf{k}$ is the direction of propagation).

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This matches the right hand rule for a current carrying wire and the induces magnetic field around the wire.

Now, for the reasons of symmetry, a radio wave also could be drawn with $\mathbf{E}$, $\mathbf{-B}$ and $\mathbf{k}$. Aplicated to the image above, the green fieldlines (which showing the direction of the magnetic field) simply would show in the opposite direction. How induce a left hand radio wave?