<p>Metamaterial-based nonreciprocity has emerged as a promising frontier for novel wave manipulation, yet most realizations rely on external biasing or auxiliary mechanisms, restricting their robustness and applicability. Here, we investigate the inherent nonreciprocity in a nonlinear metamaterial without any external apparatus. Fundamentally, since structural asymmetry governs the internal mode distribution, amplitude-dependent nonlinearity inevitably creates distinct boundary-excitations for forward and backward waves, inherently leading to nonreciprocity. To effectively combine structural asymmetry with nonlinearity, we leverage a diatomic configuration as a robust baseline, and introduce alternating nonlinear stiffnesses. We develop a rigorous analytical framework based on the Rayleigh-Schrödinger perturbation to capture the amplitude-dependent dispersion of the asymmetric unit cell. The numerical simulations validate the analytical predictions, and demonstrate direction-specific bandgap modulation for forward and backward waves. This study advances the understanding of nonlinear dynamics by elucidating how the interplay between structural asymmetry and nonlinearity passively induces non-reciprocal transmission, offering a pathway toward self-adaptive wave control systems.</p>