  We have performed the first ab-initio calculations of a possible complex
non-collinear magnetic structure in aluminium-rich Al-Mn liquids within the
real-space tight-binding LMTO method. In our previous work we predicted the
existence of large magnetic moments in Al-Mn liquids [A.M. Bratkovsky, A.V.
Smirnov, D. N. Manh, and A. Pasturel, \prb {\bf 52}, 3056 (1995)] which has
been very recently confirmed experimentally. Our present calculations show that
there is a strong tendency for the moments on Mn to have a non-collinear
(random) order retaining their large value of about 3~$\mu_B$. The d-electrons
on Mn demonstrate a pronounced non-rigid band behaviour which cannot be
reproduced within a simple Stoner picture. The origin of the magnetism in these
systems is a topological disorder which drives the moments formation and
frustrates their directions in the liquid phase.
