The majority of neutralizing antibodies (NAbs) against SARS-CoV-2 recognize the receptor-binding domain (RBD) of the spike (S) protein. As an escaping strategy, the RBD of the virus is highly variable, evolving mutations to thwart a natural immune response or vaccination. Targeting non-RBD regions of the S protein thus provides a viable alternative to generating potential, robust NAbs. Using a pre-pandemic combinatorial antibody library of 10¹¹, through an alternate negative and positive screening strategy, 11 non-RBD-targeting antibodies are identified. Amongst one NAb that binds specifically to the N-terminal domain of the S protein, SA3, shows mutually non-exclusive binding of the angiotensin-converting enzyme 2 receptor with the S protein. SA3 appears to be insensitive to the conformational change and to interact with both the “open” and “closed” configurations of the trimeric S protein. SA3 shows compatible neutralization as S-E6, an RBD-targeting NAb, against the wild type and variant of concern (VOC) B.1.351 (Beta) of the SARS-CoV-2 pseudo virus. More importantly, the combination of SA3 with S-E6 is synergistic and recovers from the 10-fold loss in neutralization efficacy against the VOC B.1.351 pseudo virus.