We synthesize and study single crystals of a new double-perovskite Sr2YIrO6. Despite two strongly unfavorable conditions for magnetic order, namely, pentavalent Ir5+(5d4) ions which are anticipated to have Jeff=0 singlet ground states in the strong spin-orbit coupling (SOC) limit, and geometric frustration in a face centered cubic structure formed by the Ir5+ ions, we observe this iridate to undergo a novel magnetic transition at temperatures below 1.3 K. We provide compelling experimental and theoretical evidence that the origin of magnetism is in an unusual interplay between strong non-cubic crystal fields and intermediate-strength SOC. Sr2YIrO6 provides a rare example of the failed dominance of SOC in the iridates.