  The letter presents a method for the reduction in the mutual coherence of an
overcomplete Gaussian or Bernoulli random matrix, which is fairly small due to
the lower bound given here on the probability of the event that the aforesaid
mutual coherence is less than any given number in (0, 1). The mutual coherence
of the matrix that belongs to a set which contains the two types of matrices
with high probability can be reduced by a similar method but a subset that has
Lebesgue measure zero. The numerical results are provided to illustrate the
reduction in the mutual coherence of an overcomplete Gaussian, Bernoulli or
uniform random dictionary. The effect on the third type is better than a former
result.
