  We propose a new method to construct a four parameter family of
quantum-mechanical point interactions in one dimension, which is known as all
possible self-adjoint extensions of the symmetric operator $T=-\Delta \lceil
C^{\infty}_{0}({\bf R} \backslash\{0\})$. It is achieved in the small distance
limit of equally spaced three neighboring Dirac's $\delta$ potentials. The
strength for each $\delta$ is appropriately renormalized according to the
distance and it diverges, in general, in the small distance limit. The validity
of our method is ensured by numerical calculations. In general cases except for
usual $\delta$, the wave function discontinuity appears around the interaction
and one can observe such a tendency even at a finite distance level.
