We have observed the anomalous longitudinal magnetoresistance conditionsR(H) = 0 and 0<R(H) <R(0) on a [111]‐oriented copper crystal specimen. The magnetoresistance voltages measured by two probe sets on mutually perpendicular faces of the specimen are observed to have a significant difference. Both of these effects are shown to be due to very slight misorientations of the specimen with respect to the magnetic field. In light of the observations, we present some precautions which should be observed in making longitudinal magnetoresistance measurements on high‐purity materials.