  This paper reports the results of an analysis of the Doppler tracking data of
Pioneer probes which did show an anomalous behaviour. A software has been
developed for the sake of performing a data analysis as independent as possible
from that of J. Anderson et al. \citep{anderson}, using the same data set. A
first output of this new analysis is a confirmation of the existence of a
secular anomaly with an amplitude about 0.8 nms$^{-2}$ compatible with that
reported by Anderson et al. A second output is the study of periodic variations
of the anomaly, which we characterize as functions of the azimuthal angle
$\varphi$ defined by the directions Sun-Earth Antenna and Sun-Pioneer. An
improved fit is obtained with periodic variations written as the sum of a
secular acceleration and two sinusoids of the angles $\varphi$ and $2\varphi$.
The tests which have been performed for assessing the robustness of these
results are presented.
