Remanent magnetization complicates the inversion of magnetic data, because it alters the direction and intensity of the magnetization vector. Remanent magnetization is impossible to ignore in many applications of magnetic method including mineral exploration particularly iron ore, geomagnetism, regional investigation, and archaeological measurements. If inversion do regardless remanence, the results will be unreliable and misleading. To reduce the effect or remanence, total field anomaly (TFA) has been transformed to total magnitude anomaly (TMA). The inversion algorithm is based on improving compact inversion method in three-dimensional. The method has been tested using synthetic and real data. The synthetic example consisting of a dipping dike buried in a nonmagnetic background. The effective susceptibility is set to 0.05 SI, and the inducing-field direction for this model has an inclination of 65°, a declination of 25°. The total magnetization with remanence has an inclination of 45° and a declination of 75°. Synthetic data inversion are consistent with the known geologic attributes of the magnetic sources.