  I study phase transitions occuring in noncollinear magnets by means of a
self-consistent screening approximation. The Ginzburg-Landau theory involves
two N-component vector fields with two independent quartic couplings allowing a
symmetry-breaking scheme which is SO(N)times SO(2) broken down to SO(N-2)times
SO(2)_diag. I find that there is a second-order phase transition in the
physical cases N=2,3, D=3 and that there is no fluctuation-induced first-order
transition. This is very similar to the case of the normal-to-superconducting
phase transition as recently found by Radzihovsky. The exponents are
eta(N=3,D=3)= 0.11, eta(N=2,D=3) =0.15 and go smoothly to the large-N limit.
