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In this work we get the presentation of the group of a link in R³ with good projection, the relators being obtained locally in à neighbourhood of the link's crossing points, a fact that minimizes the number of letters of these relators which, in turn, implies maxi mal simplification of such presentations. We also develop a systematical way of computing the presenta tion of the group of a link with good projection contained in the in terior of a solid torus of genus m. The actual computation of such presentations is illustrated by means of several examples.