It is known that in low magnetic fields the superfluid transition of ^{3}He in nematic aerogel occurs into the polar phase. Using a vibrating aerogel resonator, we observe that in high magnetic fields this transition splits into two discrete transitions, occurring at different temperatures. According to theoretical models, a new superfluid phase-the β phase-should be realized between these two transitions. The temperature range of existence of the new phase is measured as a function of magnetic field. The results are well consistent with theoretical expectations for the β phase.