Abstract: Minimization algorithms of logic function involve two main steps: generation of prime implicants and extraction of a minimal cover from those primes. It is said that the second step is more difficult than the first one, and it is true. We present a method for eliminating irredundant terms and selecting a near minimal cover with acceptable complexity. Given G, a prime cover of function F, first, we divide G into three subsets: essential primes E, complete redundances R and relative redundances P. Then we select a subset P * from P such that P*∪E is a near minimal cover of F. Clearly, the later step is much more complex than the former. And this is why the discussion is mostly on it.