A method and a system for continuously in-line annealing a forwarding ferromagnetic amorphous alloy ribbon in a curved shape to improve its magnetic properties without causing the ribbon to become brittle and which operates at significant high ribbon feeding rates. The amorphous alloy ribbon is fed forward, tensioned and guided along a path at a preset feeding rate and is heated at a point along the path at a rate greater than 103° C./sec to a temperature to initiate a thermal treatment. Then the ribbon is initially cooled at a rate greater than 103° C./sec until the thermal treatment ends. During the thermal treatment, a series of mechanical constraints is applied on the ribbon until the amorphous alloy ribbon adopts a specific shape at rest after the thermal treatment is ended. After the initial cooling, the amorphous alloy ribbon is subsequently cooled at a sufficient rate to a temperature that will preserve the specific shape.