electromagnetism - Can the two electromagnetic field tensors be combined into a more general tensor?

Given the electromagnetic field tensor

$$\begin{align} F_{\mu\nu} = \begin{pmatrix} 0 & -E_{x} & -E_{y} & -E_{z} \\ E_{x} & 0 & B_{z} & -B_{y} \\ E_{y} & -B_{z} & 0 & B_{x} \\ E_{z} & B_{y} & -B_{x} & 0 \end{pmatrix} \end{align}$$ and its dual $$\begin{align} G_{\mu\nu} = \begin{pmatrix} 0 & B_{x} & B_{y} & B_{z} \\ -B_{x} & 0 & E_{z} & -E_{y} \\ -B_{y} & -E_{z} & 0 & E_{x} \\ -B_{z} & E_{y} & -E_{x} & 0 \end{pmatrix} \,, \end{align}$$ does there exist a general tensor $H_{\mu\nu}$ that combines $F_{\mu\nu}$ and $G_{\mu\nu}$ into a more general tensor in Minikowski space?