  We address the localization of a scalar field, whose bulk-mass M is
considered in a wide range including the tachyonic region,on a three-brane. The
brane with non-zero cosmological constant $\lambda$ is embedded in five
dimensional bulk space. We find in this case that the trapped scalar could have
mass $m$ which has an upper bound and expressed as $m^2=m_0^2+\alpha M^2\leq
\beta |\lambda|$ with the calculable numbers $m_0^2, \alpha, \beta$. We point
out that this result would be important to study the stability of the brane and
cosmological problems based on the brane-world.
