The Bahía de Caráquez earthquake occurred on August of 1998. This is the most important seismic event in Ecuador in recent years. The seismograms recorded were cut at the peak points because the accelerations overcame the maximum value that was settled for the sensor.The Reduced Intersection Method is proposed to reconstruct the cut portion of the seismograms. The method is tested with of Bahía de Caráquez earthquake, cutting intentionally its accelerograms for afterward, reconstructing them. The results are filtered to eliminate ambiental noise and elastic spectras are constructed to compare the results.