Single-particle averaging from electron microscope images strongly dep
ends on alignment. Most alignment procedures are based on cross-correl
ation of an initial reference image with the rest of the population, l
eading to a clear pattern dependence. Among the different approaches t
hat have been proposed to minimize this problem, one of the most widel
y used is the so-called iterative reference-free alignment algorithm (
RFAA), proposed by Penczek et al. [Ultramicroscopy 40 (1992) 33]. To a
void the pattern dependence shown by the initial ''random approximatio
n'' step of this method, we propose a variant of the algorithm that is
more independent of the input order of the initial images and which c
ould substitute the random initialization of the RFAA.