  We study the stability constraints on the parameter space of a triplet
extension of MSSM. Existence of unbounded from below directions in the
potential can spoil successful Electroweak (EW) symmetry breaking by making the
corresponding minimum unstable, and hence the model should be free from those
directions. Avoiding those directions restricts the parameter space of the
model. We derive four stability constraints, of which only three independent
from each other. After scanning the model's parameter space for
phenomenologically viable data points, we impose the stability constraints and
find that only about a quarter of the data points features a stable EW minimum.
At those data points featuring stability, $\mu$ and the up Higgs soft mass turn
out to be smaller than about a TeV in absolute value, which make the mass of
the lightest chargino and neutralino smaller than about 700 GeV. Two relevant
phenomenological consequences of lifting the unbounded from below directions
are that the lightest Higgs boson decay rate to diphoton predicted by the
triplet extension of MSSM generally features larger deviations from MSSM and
fine tuning is actually higher, that what each of the two would be without
imposing stability constraints.
