I will show the validity of a strong unique continuation principle at certain boundary points for solutions to a class of nonlocal equations by means of the classical Almgren monotonicity approach. To be more precise, due to the nonlocal nature of the involved operator, we resort to an extension procedure which leads us to study a local problem in one dimension more; for this problem the derivation of a Almgren monotonicity formula is possible, therefore obtaining a strong unique continuation principle. An additional blow-up analysis allows us to get a strong unique continuation principle for the original nonlocal problem as well, by a classification of all the admissible vanishing orders of solutions at the boundary points.