The direction of the fields of an electromagnetic wave is determined by [Maxwell's equations](https://en.wikipedia.org/wiki/Maxwell%27s_equations). For the particular case of a _plane_ electromagnetic wave of angular frequency $\omega$ in vacuum, which can be represented by the picture you posted, Maxwell's equations require that the wave vector $\boldsymbol{k}$, the electric field $\boldsymbol{E}$ and the magnetic flux density $\boldsymbol{B}$ obey the relationships (the dot represent the scalar product and the cross the vector product)

$$\begin{align}&\boldsymbol{k}\cdot \boldsymbol{E} = 0, \\ &\boldsymbol{k}\cdot \boldsymbol{B} = 0, \\ & \boldsymbol{B}=\frac{1}{\omega}\boldsymbol{k}\times \boldsymbol{E}.\end{align}$$

This means that $\boldsymbol{k}$, $\boldsymbol{E}$ and $\boldsymbol{B}$ are three orthogonal vectors and that the direction of any one of them is determined by the other two. Therefore, no, you cannot mirror the magnetic field in the picture.