Zinc is emerging as a key material for next-generation biodegradable implants1, 2, 3, 4-5. However, its inherent softness limits its use in load-bearing orthopaedic implants. Although reducing the grain size of zinc can make it stronger, it also destabilizes its mechanical properties and thus makes it less durable at body temperature6. Here we show that extruded Zn alloys of dilute compositions can achieve ultrahigh strength and excellent durability when their micron-scale grain size is increased while maintaining a basal texture. In this inverse Hall-Petch effect, the dominant deformation mode changes from inter-granular grain boundary sliding and dynamic recrystallization at the original grain size to intra-granular pyramidal slip and unusual twinning at the increased grain size. The role of the anomalous twins, termed 'accommodation twins' in this work, is to accommodate the altered grain shape in the plane lying perpendicular to the external loading direction, in contrast to the well-known 'mechanical twins' whose role is to deliver plasticity along the external loading direction7,8. The strength level achieved in these dilute zinc alloys is nearly double those of biodegradable implants made of magnesium alloys-making them the strongest and most stable biodegradable alloys available, to our knowledge, for fabricating bone fixation implants.