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We study the Banach-Lie group $Aut(A^{-})$ of Lie automorphisms of a complex associative $H^{*}$-algebra. Also some consequences about its Lie algebra, the algebra of Lie derivations of $A$, are obtained. For a topologically simple $A$, in the infinite-dimensional case we have $Aut{(A^{-})}_0=Aut(A)$ implying $Der(A)=Der(A^{-})$. In the finite dimensional case $Aut{(A^{-})}_0$ is a direct product of $Aut(A)$ and a certain subgroup of Lie derivations $\delta$ from $A$ to its center, annihilating commutators.