We have developed a new algorithm that retrieves information about relative dip angle, relative azimuth angle, vertical resistivity, and horizontal resistivity from multicomponent EM induction logging data. To investigate how relative dip and azimuth angles affect multicomponent induction logging data, we performed a sensitivity analysis using an anisotropic whole space model. Based upon the sensitivity analysis, we designed a two-step procedure to recover relative dip, relative azimuth, horizontal resistivity, and vertical resistivity. In the first step, the observed data are transformed into a new data set independent of the azimuth angle; a simultaneous inversion method recovers relative dip angle, vertical resistivity, and horizontal resistivity. In the second step, a 1D line search is performed to decide relative azimuth angle. Synthetic and field data tests indicate that the new inversion algorithm can extract information about relative dip and azimuth angles as well as the anisotropic resistivity structure from multicomponent induction logging data.