  A very sensitive search for cosmic-ray antihelium was performed using data
obtained from three scientific flights of BESS magnetic rigidity spectrometer.
We have not observed any antihelium; this places a model-independent upper
limit (95 % C.L.) on the antihelium flux of 6*10**(-4) m**(-2)sr**(-1)s**(-1)
at the top of the atmosphere in the rigidity region 1 to 16 GV, after
correcting for the estimated interaction loss of antihelium in the air and in
the instrument. The corresponding upper limit on the Hebar/He flux ratio is
3.1*10**(-6), 30 times more stringent than the limits obtained in similar
rigidity regions with magnetic spectrometers previous to BESS.
