In this paper, new matrix inequality conditions on the terminal weighting matrices are proposed for linear continuous time-invariant systems under which nonincreasing or nondecreasing monotonicities of the optimal cost are guaranteed. It is shown that the proposed terminal inequality conditions guarantee the closed-loop stability of the receding horizon control (RHC) with additional conditions of observability or controllability. The proposed terminal inequality conditions for the cost monotonicity and the closed-loop stability in this paper include most well-known existing terminal conditions as special cases.