This flat balance spring for a horological balance comprises a wound strip shaped to ensure an approximately concentric development of the balance spring and almost zero force on the pivots and on the fixing point, during a rotation of less than 360° of its inner end relative to its outer end in both directions from its rest position. The stiffness of its strip decreases gradually and through more than 360° from each of its two ends, the lowest stiffness being situated in the median part of the strip.