  Context: In 2004, changes in the radio morphology of the Be/X-ray binary
system LSI+61303 suggested that it is a precessing microquasar. In 2006, a set
of VLBA observations performed throughout the entire orbit of the system were
not used to study its precession because the changes in radio morphology could
tentatively be explained by the alternative pulsar model. However, a recent
radio spectral index data analysis has confirmed the predictions of the
two-peak microquasar model, which therefore does apply in LSI+61303. Aims: We
revisit the set of VLBA observations performed throughout the orbit to
determine the precession period and improve our understanding of the physical
mechanism behind the precession. Methods: By reanalyzing the VLBA data set, we
improve the dynamic range of images by a factor of four, using
self-calibration. Different fitting techniques are used and compared to
determine the peak positions in phase-referenced maps. Results: The improved
dynamic range shows that in addition to the images with a one-sided structure,
there are several images with a double-sided structure. The astrometry
indicates that the peak in consecutive images for the whole set of observations
describes a well-defined ellipse, 6-7 times larger than the orbit, with a
period of about 28 d. Conclusions: A double-sided structure is not expected to
be formed from the expanding shocked wind predicted in the pulsar scenario. In
contrast, a precessing microquasar model can explain the double- and one-sided
structures in terms of variable Doppler boosting. The ellipse defined by the
astrometry could be the cross-section of the precession cone, at the distance
of the 8.4 GHz-core of the steady jet, and 28d the precession period.
