In the paper the set of all words of length $n$ is constructed and enumerated, over any alphabet $A$ with a forbidden fixed subword $a_1a_2\dots a_k$ which is $a$ good word i.e. $a_1a_2/dots a_s\neq a_{k-s+1}a_{k-s+2}\dots a_k$ for each natural number $s<k$. This number of words is counted in two different ways, which gives new combinatorial identities.