  The type II seesaw mechanism for neutrino mass generation usually makes use
of one complex scalar triplet. The collider signature of the doubly-charged
scalar, the most striking feature of this scenario,consists mostly in decays
into same-sign dileptons or same-sign $W$ boson pairs. However, certain
scenarios of neutrino mass generation, such as those imposing texture zeros by
a symmetry mechanism, require at least two triplets in order to be consistent
with type-II the seesaw mechanism. We develop a model with two such complex
triplets and show that, in such a case, mixing between the triplets can cause
the heavier doubly-charged scalar mass eigenstate to decay into a
singly-charged scalar and a $W$ boson of the same sign. Considering a large
number of benchmark points with different orders of magnitude of the $\Delta L
=2$ Yukawa couplings, chosen in agreement with the observed neutrino mass and
mixing pattern, we demonstrate that $H^{++}_1 \rightarrow H^+_2 W^+$ can have
more than 99% branching fraction in the cases where the vacuum expectation
values of the triplets are small. The implications of this for the LHC are
pointed out.
