  In this paper, a new conserved current for Klein-Gordon equation is derived.
It is shown, for $1+1$-dimensions, the first component of this current is
non-negative and reduces to $|\phi|^2$ in non-relativistic limit. Therefore, it
can be interpreted as the probability density of spinless particles. In
addition, main issues pertaining to localization in relativistic quantum theory
are discussed, with a demonstration on how this definition of probability
density can overcome such obstacles. Our numerical study indicates that the
probability density deviates significantly from $|\phi|^2$ only when the
uncertainty in momentum is greater than $m_0c$.
