Magnetic field measurements obtained by the Pioneer Venus orbiter at low altitudes in the solar wind wake region are examined to search for possible surface-correlated features and any possible intrinsic magnetic moment. The observed field variations in the wake do not resemble our expectations for a solar wind interaction wiht even a weak intrinsic magnetic field. There is little orbit-to-orbit persistance of features in the magnetic records. The magnetic field measurements in the wake have been averaged in 10¿¿10¿ bins to minimize the effects of external field sources. The average fields in these 37 bins appear to be randomly oriented and consistent with zero mean in the region mapped. Using these 37 averaged vector fields, we obtained a maximum intrinsic magnetic dipole moment of 4.3¿2.0¿1021 G cm3, approximately an order of magnitude less than previous estimates. A more conservative estimate of the probable error of the mean is 5.5¿1021 G cm3. Thus the Pioneer Venus measurements are consistent with zero planetary moment. The present measurements are also far below estimates based on angular momentum, the so-called 'magnetic Bode's law,' and far below the dynamo scaling law of Busse.