A method is described of making an electrically programmable integrated circuit which comprises meltable contact bridges (22) between selected connecting points. In the method, firstly in a semiconductor substrate (10) by means of diffusion or ion implantation to obtain desired circuit functions a semiconductor structure with zones (12) of different conductivity type is formed. On the surface of the semiconductor structure a first protective layer (14) is formed in which contact windows (18) to the selected connecting points are then formed. On the surface of the first protective layer (14) and in the contact windoews (18) a through conductive layer (20) is made of a material forming the fusible contact bridges (22). Using a plasma etching method the conductive layer (20) is etched away so that only the contact bridges (22) with an associated connecting end (21) and conductor regions leading from the contact bridges (22) to the connecting points in the contact windows (18) remain. On the remaining conductor regions a second protective layer (24) is formed which is then etched away by means of a plasma etching method except for the regions lying over the contact bridges (22). In the region of the contact windows (18) and on the connecting ends (21) of the contact bridges (22) a connecting metallization (26, 28) is then applied.