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Transversal oscillations of spicules axes may be related to the propagation of magnetohydrodynamic waves along them. These waves may become unstable and the instability can be of the Kelvin-Helmholtz type. We use the dispersion relation of kink mode derived from linearized magnetohydrodynamic equations. The input parameters of the derived dispersion equation, namely, spicules and their ambient medium densities ratios as well as their corresponding magnetic fields ratios, are considered to be within the range $0-1$. By solving the dispersion equation numerically, we show that for higher densities and lower magnetic fields ratios within the range mentioned, the KHI onset in type II spicules conditions is possible. This possibility decreases with an increase in Alfven velocity inside spicules. A rough criterion for appearing of Kelvin-Helmholtz instability is obtained. We also drive a more reliable and exact criterion for KHI onset of kink waves.