An approximate inversion, using a specific model, of Apollo subsatellite vector magnetometer data has provided estimates for the locations, scale sizes, and magnetization characteristics of strongly magnetized lunar crustal materials across a portion of the lunar far side. The nearly model-independent local bulk directions of magnetization, while otherwise random, exhibit a tendence to lie in or near planes perpendicular to the present lunar spin axis. The apparent existence of such a preferred plane of magnetization must be regarded as unfavorable for proposed local, presumably random sources of large-sclae, coherent magntization and implies that any assumed internal magnetizing dipole or external linear magnetizing field must also have been oriented mainly perpendicular to the present spin axis. The otherwise random orientations of these vectors when projected onto the equatorial plane suggests a simple explanation for the negligible lunar global dipole moment.