  We propose a novel neutrino mixing pattern in terms of only two small
integers 1 and 2 together with their square roots and the imaginary number $i$.
This ansatz is referred to as the "tetra-maximal" mixing because it can be
expressed as a product of four rotation matrices, whose mixing angles are all
\pi/4 in the complex plane. It predicts \theta_{12} = \arctan(2-\sqrt{2})
\approx 30.4^\circ, \theta_{13} = \arcsin[(\sqrt{2}-1)/(2\sqrt{2})] \approx
8.4^\circ, \theta_{23} = 45^\circ and \delta =90^\circ in the standard
parametrization, and the Jarlskog invariant of leptonic CP violation is found
to be {\cal J} = 1/32. These results are compatible with current data and can
soon be tested in a variety of neutrino oscillation experiments. Implications
of the tetra-maximal neutrino mixing on the decays of doubly-charged Higgs
bosons H^{\pm\pm} -> l^\pm_\alpha l^\pm_\beta (for \alpha, \beta = e, \mu,
\tau) are also discussed in the triplet seesaw mechanism at the TeV scale,
which will be explored at the upcoming LHC.
