  In this paper we continue to study actions of high-dimensional Lie groups on
complex manifolds. We give a complete explicit description of all pairs
$(M,G)$, where $M$ is a connected complex manifold $M$ of dimension $n\ge 2$,
and $G$ is a connected Lie group of dimension $n^2+1$ acting effectively and
properly on $M$ by holomorphic transformations. This result complements a
classification obtained earlier by the first author for $n^2+2\le\hbox{dim}
G<n^2+2n$ and a classical result due to W. Kaup for the maximal group dimension
$n^2+2n$.
