This paper reports on a magnetic field phenomenon, hereafter referred to as null fields, which were discovered during the inbound pass of the recent flyby of Jupiter by the Ulysses spacecraft. These null fields which were observed in the outer dayside magnetosphere are characterized by brief but sharp decreases of the field magnitude to values less than 1 nT. The nulls are distinguished from the current sheet signatures characteristic of the middle magnetosphere by the fact that the field does not reverse across the event. A field configuration is suggested that accounts for the observed features of the events.