It is shown that the fraction f(u) of imaginary-frequency instantaneous nor
mal modes (INM) may be defined and calculated in a random energy model (REM
) of liquids. The configurational entropy S-c and the averaged hopping rate
among the states, R, are also obtained and related to f(u), with the resul
ts R similar to f(u) and S-c = a + b ln(f(u)). The proportionality between
R and f(u) is the basis of existing INM theories of diffusion, so the REM f
urther confirms their validity. A link to S-c opens new avenues for introdu
cing INM into dynamical theories. Liquid states are usually defined by assi
gning a configuration to the minimum to which it will drain, but the REM na
turally treats saddle barriers on the same footing as minima, which may be
a better mapping of the continuum of configurations to discrete states. Req
uirements for a detailed REM description of liquids are discussed.