  In this study, 36 cores (30 starless and 6 protostellar) identified in Orion
were surveyed to search for inward motions. We used the Nobeyama 45 m radio
telescope, and mapped the cores in the $J = 1\rightarrow0$ transitions of
HCO$^+$, H$^{13}$CO$^+$, N$_2$H$^+$, HNC, and HN$^{13}$C. The asymmetry
parameter $\delta V$, which was the ratio of the difference between the HCO$^+$
and H$^{13}$CO$^+$ peak velocities to the H$^{13}$CO$^+$ line width, was biased
toward negative values, suggesting that inward motions were more dominant than
outward motions. Three starless cores (10% of all starless cores surveyed) were
identified as cores with blue-skewed line profiles (asymmetric profiles with
more intense blue-shifted emission), and another two starless cores (7%) were
identified as candidate blue-skewed line profiles. The peak velocity difference
between HCO$^+$ and H$^{13}$CO$^+$ of them was up to 0.9 km s$^{-1}$,
suggesting that some inward motions exceeded the speed of sound for the
quiescent gas ($\sim10-17$ K). The mean of $\delta V$ of the five
aforementioned starless cores was derived to be $-$0.5$\pm$0.3. One core,
G211.16$-$19.33North3, observed using the ALMA ACA in DCO$^+$ $J =
3\rightarrow2$ exhibited blue-skewed features. Velocity offset in the
blue-skewed line profile with a dip in the DCO$^+$ $J = 3\rightarrow2$ line was
larger ($\sim 0.5$ km s$^{-1}$) than that in HCO$^+$ $J = 1\rightarrow0$ ($\sim
0.2$ km s$^{-1}$), which may represent gravitational acceleration of inward
motions. It seems that this core is at the last stage in the starless phase,
judging from the chemical evolution factor version 2.0 (CEF2.0).
