  We investigate $S=-2$ production from the $\Lambda p\to K^+X$ reactions
within the effective Lagrangian approach. The $\Lambda p\to K^+\Lambda\Lambda$
and $\Lambda p\to K^+\Xi^-p$ reactions are considered to find the lightest
$S=-2$ system, which is $H$-dibaryon. We assume that the
$H(2250)\to\Lambda\Lambda$, and $H(2270)\to\Xi^-p$ decays with the intrinsic
decay width of 1 MeV. According to our calculations, the total cross-sections
for $\Lambda p\to K^+\Lambda\Lambda$ and $\Lambda p\to K^+\Xi^-p$ reactions
were found to be of the order of a few $\mu$b in the $\Lambda$ beam momentum
range of up to 5 GeV$/c$. Furthermore, the direct access of information
regarding the interference patterns between the $H$-dibaryon and non-resonant
contributions was demonstrated.
