A numerical semigroup is a subset S of closed under addition, containing the identity element of and generating as a group (here denotes the set of nonnegative integers and the set of integer numbers). If S is a numerical semigroup, then it admits a unique minimal system of generators n0< n1<···< np. The Apéry set of S with respect n0 is the set s∈ S s− n0∈ S. If s∈ S, then there exists a0 a1 ap∈ p+ 1 such that s= a0n0+ a1n1+···+ apnp. We say that an element has a unique expression whether a0 a1 ap is unique. In this paper we are interested only in numerical semigroups fufilling that all the elements of its Apéry set with respect n0 have a unique expression. The main result of this work is Theorem 1. That gives us a minimal presentation for this kind of semigroup. As an application of this theorem, we study the minimal presentations of symmetric numerical semigroups fulfilling that all the elements of its Apéry set, except the maximum, have a unique expression. All the methods used in this work are semigroupist and they are in the same line