We show that the R~((3))δK operator in effective field theory is significant for avoiding the instability of nonsingular bounce, where R~((3)) and K_(μν) are the three-dimensional Ricci scalar and the extrinsic curvature on the spacelike hypersurface, respectively. We point out that the covariant Lagrangian of R~((3))δK, i.e., L_(R~((3))δK), has the second order derivative couplings of scalar field to gravity which do not appear in Horndeski theory or its extensions but does not bring the Ostrogradski ghost. We also discuss the possible effect of L_(R~((3))δK) on the primordial scalar perturbation in the inflation scenario.
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