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The neutral triplet scalars (H^0, A^0) in the Higgs Triplet Model (HTM) aredifficult to detect at the LHC for the case of mass degeneracy with the singlycharged (H^+) and doubly charged (H^++) scalars.  A non-zero value of a specific quartic coupling in the scalar potentialremoves this degeneracy, and positive values of this coupling would give riseto the mass hierarchy m_{A^0,H^0} > m_{H^+} > m_{H^++}.  In this scenario the decays H^0-> H^+ W^* and A^0-> H^+ W^*, followed by H^+-> H^{++} W^*, can proceed with large branching ratios, even for small masssplittings among the triplet scalars.  Such a cascade process would lead to production of H^{++}H^{--} accompaniedby several virtual W bosons, and would provide a way of observing H^0 and A^0with a signature which is different from that of the conventional productionprocess for doubly charged scalars, q qbar -> \gamma^*, Z^* -> H^{++}H^{--}.  Assuming the decay H^{++} to l^+ l^+, we quantify the magnitude of thefive-lepton and six-lepton signals in these channels, which have essentiallynegligible backgrounds at the LHC.

Five-lepton and six-lepton signatures from production of neutral triplet scalars in the Higgs Triplet Model