In this work we present dependence of AC losses in a YBCO tape conductor carrying an AC transport current in an external AC magnetic field on the angle between the direction of the external field and the tape face of the conductor. The losses were measured by a calorimetric method whose validity was proven by simultaneous electric and calorimetric measurements of the losses in the same part of the conductor. The experiment was conducted at 77 K. The measured data show that the AC losses are dominated by the normal component of the external magnetic field to the tape surface. It is also shown that the AC losses sharply drop when the external magnetic field is parallel to the tape surface, which is due to extremely high aspect ratio of the YBCO conductor.