  We re-examine the commonly used density functional theory plus Hubbard
\textit{U} (DFT$+U$) method for the case of non-collinear magnets. While many
studies neglect to explicitly include the exchange correction parameter
\textit{J}, or consider its exact value to be unimportant, here we show that in
the case of non-collinear magnetism calculations the \textit{J} parameter can
strongly affect the magnetic ground state. We illustrate the strong
\textit{J}-dependence of magnetic canting and magnetocrystalline anisotropy by
calculating trends in the magnetic lithium orthophosphate family LiMPO$_4$ (M =
Fe and Ni) and difluorite family MF$_2$ (M = Mn, Fe, Co and Ni). Our results
can be readily understood by expanding the usual DFT$+U$ equations within the
spinor scheme, in which the \textit{J} parameter acts directly on the
off-diagonal components which determine the spin canting.
