  The Tree Augmentation Problem (TAP) is: given a connected graph $G=(V,{\cal
E})$ and an edge set $E$ on $V$ find a minimum size subset of edges $F
\subseteq E$ such that $(V,{\cal E} \cup F)$ is $2$-edge-connected. In the
conference version \cite{EFKN-APPROX} was sketched a $1.5$-approximation
algorithm for the problem. Since a full proof was very complex and long, the
journal version was cut into two parts. In the first part \cite{EFKN-TALG} was
only proved ratio $1.8$. An attempt to simplify the second part produced an
error in \cite{EKN-IPL}. Here we give a correct, different, and self contained
proof of the ratio $1.5$, that is also substantially simpler and shorter than
the previous proofs.
