The lattice fermion determinants, in a given background gauge field, a
re evaluated for two different kinds of random lattices and compared t
o those of naive and wilson fermions in the continuum limit. While the
fermion doubling is confirmed on one kind of lattices, there is posit
ive evidence that it may be absent for the other, at least for vector
interactions in two dimensions. Combined with previous studies, arbitr
ary randomness by itself is shown to be not a sufficient condition to
remove the fermion doublers.