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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 $δV$, 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 $δV$ 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).