We have developed an inversion method to recover the depth and the total magnetization intensity of the basement under a sedimentary basin using the amplitude of the magnetic anomaly vector (amplitude data). Because the amplitude data are weakly dependent on the magnetization direction, our method is suitable for interpreting areas with remanent magnetization. Our method assumes constant magnetized basement rocks overlain by nonmagnetic sediments. To overcome the inherent ambiguity of potential field data, we assume knowledge of the average depth of the basement and use it as a constraint to regularize the inversion. A sensitivity analysis with synthetic data shows the weak dependency of the magnetic amplitude inversion on the magnetization direction. Different combinations of magnetization directions recover the interface separating sediments from basement rocks. Test on field data over the Foz do Amazonas Basin, Brazil, recovers the shape of the basement relief without any knowledge about the magnetization intensity and direction. The estimated basement relief reveals a smooth basement framework with basement highs in the central part of the area. In a regional-scale perspective, the deeper and constant estimated basement relief at the northernmost limit of the area may suggest changing in crustal domains from a hyperextended continental crust to homogeneous oceanic crust.