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Let H be a Weierstrass semigroup, i.e., the set HðPÞ of integers which are pole orders at P of regular functions on CnfPg for some pointed non-singular curve ðC; PÞ. In this paper for any Weierstrass semigroup H we construct a double covering p : C C ! C with a ramification point P P such that Hðpð P PÞÞ ¼ H. We also determine the semigroup Hð P PÞ. Moreover, in the case where H starts with 3 we investigate the relation between the semigroup Hð P PÞ and the Weierstrass semigroup of a total ramification point on a cyclic covering of the projective line with degree 6.