A data set of 18,000 low-altitude nightside vector measurements from the Pioneer Venus Orbiter (PVO) magnetometer is used to establish a new upper limit on the intrinsic dipolar magnetic moment of Venus. Various techniques are used to search for coherence in the magnetic observations which might be attributable to such an intrinsic field, with negative results. A similar search is conducted for surface magnetism, that is, geographically correlated magnetic features, also with negative results. The present study represents the best limits that PVO observations can provide and is limited by the amount of low-altitude nightside data available. We do not expect to obtain a significant amount of new low-altitude data later in the mission. Our new upper limit to the magnetic moment is 8.4¿1010 T m3 or about 10-5 of the terrestrial magnetic moment. This is a factor of 4 lower than the previous upper limit. ¿American Geophysical Union 1987