A measurement of the transverse-transverse, C TT , and transverse-normal C TN , τ spin correlations in the decay Z 0 → τ + τ − is presented based on the aplanarity angle of the decay products of both taus. Based on 80 pb −1 of data collected by ALEPH[1] in 1992, 1993 and 1994 on the peak of the Z resonance, the results are: C TT = 1.00 ± 0.14( stat ) ± 0.04( syst ), C TN =−0.08 ± 0.14( stat ) ± 0.02( syst ). These values are in agreement with the Standard Model predictions, C TT = 0.989 and C TN = 0.