  The OPERA neutrino experiment is designed to perform the first observation of
neutrino oscillations in direct appearance mode in the $\nu_\mu \to \nu_\tau$
channel, via the detection of the $\tau$-leptons created in charged current
$\nu_\tau$ interactions. The detector, located in the underground Gran Sasso
Laboratory, consists of an emulsion/lead target with an average mass of about
1.2 kt, complemented by electronic detectors. It is exposed to the CERN
Neutrinos to Gran Sasso beam, with a baseline of 730 km and a mean energy of 17
GeV. The observation of the first $\nu_\tau$ candidate event and the analysis
of the 2008-2009 neutrino sample have been reported in previous publications.
This work describes substantial improvements in the analysis and in the
evaluation of the detection efficiencies and backgrounds using new simulation
tools. The analysis is extended to a sub-sample of 2010 and 2011 data,
resulting from an electronic detector-based pre-selection, in which an
additional $\nu_\tau$ candidate has been observed. The significance of the two
events in terms of a $\nu_\mu \to \nu_\tau$ oscillation signal is of 2.40
$\sigma$.
