  We study the fraction $f$ of nucleotides involved in the formation of a
cactus--like secondary structure of random heteropolymer RNA--like molecules.
In the low--temperature limit we study this fraction as a function of the
number $c$ of different nucleotide species. We show, that with changing $c$,
the secondary structures of random RNAs undergo a morphological transition:
$f(c)\to 1$ for $c \le c_{\rm cr}$ as the chain length $n$ goes to infinity,
signaling the formation of a virtually "perfect" gapless secondary structure;
while $f(c)<1$ for $c>c_{\rm cr}$, what means that a non-perfect structure with
gaps is formed. The strict upper and lower bounds $2 \le c_{\rm cr} \le 4$ are
proven, and the numerical evidence for $c_{\rm cr}$ is presented. The relevance
of the transition from the evolutional point of view is discussed.
