  A Carter like constant for the geodesic motion in the $Y(p,q)$
Einstein-Sasaki geometries is presented. This constant is functionally
independent with respect to the five known constants for the geometry. Since
the geometry is five dimensional and the number of independent constants of
motion is at least six, the geodesic equations are superintegrable. We point
out that this result applies to the configuration of massless geodesic in
$AdS_5\times Y(p,q)$ studied by Benvenuti and Kruczenski, which are matched to
long BPS operators in the dual N=1 supersymmetric gauge theory.
