The directional correlation of the 346-136 Kev gamma-gamma cascade in Ta¹⁸¹ was measured using the delayed coincidence method with a source of Hf¹⁸¹ in 27 N HF. The contributions to the composite delayed coincidence spectrum of the interfering 133-482 Kev and 133 - 346 Kev cascades were removed by the subtraction from this spectrum of appropriate 133-482 Kev pure delayed coincidence data. The extracted 346 -136 Kev coincidence data then yielded the correlation coefficients A₂₂ = o.190 土0.011 and A₄₄. = -0.025 土O. 024 that are consistent with the established spin sequence 5/ 2(E2)9 / 2(Ml +E2)7 / 2 and with an admixture of 16.20/0土1. 2% E2 radiation in the 136 Kev mixed transition. The results of the experiment are in excellent agreement with those obtained from conversion electron measurements and resolve the discrepancy apparent in earlier work on the 346-136 Kev cascade