  We revisit the antiferromagnetic structure of $\rm Tb_{14}Ag_{51}$ [P.
Fischer., $et\, al$. (2005). PRB, 72 134413] with the propagation vector
$[{1\over3},{1\over3},{0}] $ and parent space group $P6/m$ using both magnetic
symmetry and irreducible representation arguments. We have found a new magnetic
structure under the hexagonal Shubnikov magnetic space group $P\bar{6}'$, which
fits much better the experimental data. This new solution was obtained by
constraining the spin arrangement to one of the three possible magnetic space
groups of maximal symmetry that can be realised by a magnetic ordering
transforming according to the 4-dimensional physically irreducible
representation that is known to be relevant in this magnetic phase. The refined
model, parameterised under $P\bar{6}'$, implicitly includes the presence of a
third harmonic with the propagation vector at the gamma point $[0,0,0]$, which
has an important weight in the final result. The structure consists of 13
symmetry-independent Tb magnetic moments with the same size of $8.48(2)\mu_B$,
propagating cycloidally in the $ab$-plane. The modulation has a substantial
deviation from being purely sinusoidal due to the contribution of the mentioned
third harmonic.
