The novel iron-based compound, BaYFeO4, crystallizes in the Pnma space group with two distinct Fe3+ sites, that are alternately corner-shared [FeO5](7-) square pyramids and [FeO6](9-) octahedra, forming into [Fe4O18](24-) rings, which propagate as columns along the b-axis. A recent report shows two discernible antiferromagnetic (AFM) transitions at 36 and 48 K in the susceptibility, yet heat capacity measurements reveal no magnetic phase transitions at these temperatures. An upturn in the magnetic susceptibility measurements up to 400 K suggests the presence of short-range magnetic behavior at higher temperatures. In this Article, variable-temperature neutron powder diffraction and high-temperature magnetic susceptibility measurements were performed to clarify the magnetic behavior. Neutron powder diffraction confirmed that the two magnetic transitions observed at 36 and 48 K are due to long-range magnetic order. Below 48 K, the magnetic structure was determined as a spin-density wave (SDW) with a propagation vector, k = (0, 0, 1/3), and the moments along the b-axis, whereas the structure becomes an incommensurate cycloid [k = (0, 0, 0.35)] below 36 K with the moments within the bc-plane. However, for both cases the ordered moments on Fe3+ are only of the order similar to 3.0 mu(B), smaller than the expected values near 4.5 mu(B), indicating that significant components of the Fe moments remain paramagnetic to the lowest temperature studied, 6 K. Moreover, new high-temperature magnetic susceptibility measurements revealed a peak maximum at similar to 550 K indicative of short-range spin correlations. It is postulated that most of the magnetic entropy is thus removed at high temperatures which could explain the absence of heat capacity anomalies at the long-range ordering temperatures. Published spin dimer calculations, which appear to suggest a k = (0, 0, 0) magnetic structure, and allow for neither low dimensionality nor geometric frustration, are inadequate to explain the observed complex magnetic structure.