In this letter, a constant-amplitude biorthogonal multicode (CABM) modulation is proposed. The proposed modulation is a biorthogonal modulation scheme that employs a constant-amplitude transmission of multicode signals by introducing a simple constant-amplitude coding scheme with redundant bits. The proposed CABM modulation can provide bandwidth efficiency up to the level (i.e., 9/16) of constant-amplitude orthogonal multicode (CAOM) modulation. We prove that our encoding scheme proposed in this letter provides this constant amplitude property. The bit-error rate (BER) performance expressions and the union bounds of the proposed CABM modulation and demodulation pairs are derived analytically. The results of the computer simulation and theoretical analysis performed show that the BER performance and the hardware complexity of the proposed CABM modulation are significantly better than those of a CAOM modulation