<p>Subdomain decomposition along with Heterogeneous Asynchronous Time Integrator, such as the GC (Gravouil and Combescure) method, allows us to adopt the most appropriate time integrator and time step size depending on subdomains. The paper presents an improved version of the GC method employed for various applications ranging from impact dynamics to fluid–structure interaction problems. The proposed method, called BLG method, is based on the kinematic continuity at the fine time scale, as inherited from the progenitor GC method, guaranteeing an easy application to problems whose nonlinearities are taken into account at the fine time scale. Properties of the new BLG method in terms of stability, local truncation error, numerical damping and period elongation are thoroughly assessed thanks to a detailed spectral study of the amplification matrix related to the split oscillator. The BLG method turns out to be second-order accurate when coupling second-order accurate time integrators from the Newmark family, gaining one order with respect to the GC method. Multi-time step explicit/implicit and explicit/explicit coupling with the BLG method are considered as the most interesting cases for promising applications in nonlinear structural dynamics with impacts and complex fluid–structure interaction problems.</p>