Abstract: Interface effect in complex oxide thin-film heterostructures lies at the vanguard of current research to design technologically relevant functionality and explore emergent physical phenomena. While most of the previous works focus on the perovskite/perovskite heterostructures, the study of perovskite/brownmillerite interfaces remains in its infancy. Here, we investigate spontaneously stabilized perovskite-ferromagnet (SrCoO3-delta)/brownmillerite-antiferromagnet (SrCoO2.5) bilayer with T-N > T-C and discover an unconventional interfacial magnetic exchange bias effect. From magnetometry investigations, it is rationalized that the observed effect stems from the interfacial ferromagnet/antiferromagnet coupling. The possibility for coupled ferromagnet/spin-glass interface engendering such effect is ruled out. Strikingly, a finite coercive field persists in the paramagnetic state of SrCoO3-delta,whereas the exchange bias field vanishes at T-C . We conjecture the observed effect to be due to the effective external quenched staggered field provided by the antiferromagnetic layer for the ferromagnetic spins at the interface. Our results not only unveil a paradigm to tailor the interfacial magnetic properties in oxide heterostructures without altering the cations at the interface, but also provide a purview to delve into the fundamental aspects of exchange bias in such unusual systems, paving a big step forward in thin-film magnetism.