  The invariant mass method is used to identify the $^8$Be and $^9$B nuclei and
Hoyle state formed in dissociation of relativistic nuclei in a nuclear track
emulsion. It is shown that to identify these extremely short-lived states in
the case of the isotopes $^9$Be, $^{10}$B, $^{10}$C, $^{11}$C, $^{12}$C, and
$^{16}$O, it is sufficient to determine the invariant mass as a function of the
angles in pairs and triples of He and H fragments in the approximation of the
conservation of momentum per nucleon of the parent nucleus. According to the
criteria established in this way, the contribution of these three unstable
states was evaluated in the relativistic fragmentation of the $^{28}$Si and
$^{197}$Au nuclei.
