Vision favors head stabilization in space during perturbations of standing balance. This is particularly obvious under conditions of continuous predictable perturbations as during sinusoidal antero-posterior (A-P) translations of the supporting platform. We tested here the hypothesis that under this condition the head can instead undergo large A-P oscillations, when a precision visual task is concurrently performed. We compared the head oscillations across four conditions while standing on a continuously translating platform. Eyes open (EO, no visual task), EO while reading a text fixed to the moving platform (EO-TP), EO while reading a text fixed to earth-ground (EO-TG), eyes-closed (EC). The platform translated at 0.2 and 0.6 Hz. Participants were young adult subjects, who received no particular instruction except reading the text aloud when required. Markers fixed on head, platform and text-sheet were captured by an optoelectronic device. We found that head oscillations were larger with EC than under all EO conditions. The oscillations were the least with EO and EO-TG, and intermediate with EO-TP. This was true under both low and high translation frequency, in spite of broadly smaller head oscillations at high frequency, common to all visual conditions. The distance between the head and the text was quite constant with EO-TP but fluctuated with EO-TG. The basic whole-body coordination features were moderately similar under all conditions, as assessed by the head-platform correlation coefficients and time lags. It appears that vision does not produce head stabilization in space when a concurrent visual task requiring focusing on a reading-text moving with the platform is performed. Contrary to traditional views centered on the stabilizing effect of vision under both static and dynamic conditions, the results show that head stabilization, normally ensuring a reference for inertial guidance for body balance, can be revoked by the CNS to allow performance of a non-postural task. This novel paradigm can shift long-standing views on the effect of vision on equilibrium control and be considered a potential exercise treatment for enhancing the multisensory integration process in people with balance problems.