Christofides Algorithm - TSP, Problem in transforming AGM into a graph with all vertices of even degree

I'm implementing the Christofides algorithm and I'm getting the data from TSPLIB. the Christofides Algorithm has the following steps:

I was doing the algorithm and I got to step 5, however, only then I realized that the marriage of the vertices I was finding was not the perfect one, which is done in the following code:

int** adicionar_CM_na_AGM(int **m, int **agm, int qVgi, int *vGi,int n){
int menor =99999,v1=0,v2=0,verticeMenor;
int *aux = (int *) calloc(qVgi, sizeof(int));
for(int i=0; i<qVgi; i++)
{
    for(int j=0; j<qVgi; j++)
    {
        if(vGi[i] != vGi[j] && menor > m[vGi[i]][vGi[j]] && aux[vGi[i]] != 1 && aux[vGi[j]] != 1)
        {
            printf("%d O %d\n", i, m[vGi[i]][vGi[j]]);
            v1 = vGi[i];
            v2 = vGi[j];
            menor = m[vGi[i]][vGi[j]];
        }
    }
    aux[v1]= 1;//cria a situação de já visitados
    aux[v2]= 1;
    agm[v1][v2] = m[v1][v2];//adiciona na AGM as arestas dos vGi
    agm[v2][v1] = m[v2][v1];
    menor =9999;
}
return agm;

where: m: adjacency matrix with the distances of the vertices

agm: AGM adjacency matrix of m

qVgi: integer representing the number of odd-degree vertices

vGi: vector containing vertex numbers that have odd degrees

n: integer that represents the total vertex number of the matrix m

I would like to know if anyone would have ideas so that I can find the perfect minimum marriage of the odd grade vertices of my graph.