The invention relates to a longitudinal flexible heating mat. The inventive mat comprises a thin conductive metal strip (3) which is intended to be supplied with electric current at the ends (C, D) thereof and which is trapped between two flexible, insulating sheets (1, 1'). The mat is characterised in that: (i) the conductive strip comprises at least two elements (3a, 3b) which extend from one of the longitudinal ends (A) of the mat to the other longitudinal end (B) of same, (ii) the first ends (C, D) of the aforementioned elements are intended to be connected to respective electric power terminals, and (iii) the second ends (D, E) of said elements are free and intended to be connected to one another using connection means (7). The invention also relates to a method of producing one such mat.