We suggest that in a halo nucleus, the B-decay of a core may lead to t
he formation of a product nucleus with a similar cluster structure. As
an example, the beta-decay of Be-14 (= Be-12+n+n) is considered. Calc
ulations of the B-14 spectrum within the generator coordinate method (
GCM) predict the existence of 0(+), 1(+) and 2(+) narrow states having
a B-12+n+n structure and located near the two-neutron threshold. As f
ollows from the calculations, the B-decay of(14)Be to the 1(+) state m
ainly occurs when two halo neutrons stay far away from the core.