The reordering mechanism from the antiferromagnetic phase AFI to the antiferromagnetic phase AFII in an oxygen-deficient YBa2Cu2.94Al0.06O6+delta single crystal with an oxygen content delta=0.18 in the Cu(1) layer has been studied by neutron diffraction and nuclear quadrupole resonance (NQR). The crystal orders magnetically from the paramagnetic state to the antiferromagnetic AFI state at the Neel temperature T-N=403 K with an empirical critical exponent of beta = 0.26. Reordering to the antiferromagnetic AFII state sets in at T-2 = 12 K. In both the AFI and AFII phases the ordered magnetic moments on the Cu(2) lattice sites are identical and take a value of [S](Cu(2))approximate to 0.56 mu(B); no ordered moment is found on the Cu(1) lattice sites. From the temperature dependence of the Cu(1) NQR spectrum, the magnetic hyperfine field at Cu(1) sites is found to vary continuously as a function of temperature. This result indicates unequivocally that the AFI<->AFII reordering takes place via a noncollinear intermediate turn angle phase AFI+II.