The incommensurate magnetic structure (0.47, 0, 0.49) of NaYNiWO6 exhibits unconventional spin-density waves (SDWs) along the [100] direction, in which up and down spins alternate in each half-wave. This is in contrast to conventional SDWs, in which only one type of spin is present in each half-wave. We probed the formation of these unconventional SDWs by evaluating the spin exchanges of NaYNiWO6 based on density functional theory calculations and analyzing the nature of the spin frustration in NaYNiWO6 and by noting that a SDW is a superposition of two cycloids of opposite chirality. The unconventional SDWs along the [100] direction originate from the spin-frustrated antiferromagnetic chains of Ni( )(2+)ions along that direction, leading to conventional SDWs along the [101] direction and unconventional SDWs along the [001] direction.