The method of stochastic inversion, previously applied to modeling the secular variation and to modeling the main field, is extended to the simultaneous inversion for both main field and secular variation. A priori information is specified in a form analogous to that used previously in studies of the main field and of the secular variation; the time dependency is represented by an expansion in Legendre polynomials, resulting in a simple diagonal form for the a priori covariance matrix. With the field expanded spatially to spherical harmonic degree 14 and temporally to degree 8 the resultant inverse problem has over 2000 parameters: solution of such a large system by conventional means requiring the formation of normal equations is prohibitively expensive on all but a few machines. Alternative means of solution are required: an efficient algorithm, the preconditioned memoryless Broyden-Fletcher-Goldfarb-Shanno algorithm, which exploits the partially known eigenvalue structure of the problem, is adopted. The method is applied to the analysis of observatory data spanning the period 1900--1980. The resulting model, MFSV/1900/1980/OBS, fits the data over this long time span to better than 30 nT, while providing temporally and spatially smoothly varying models of the magnetic field at the core-mantle boundary. The model compares very favorably with other models of the main field and secular variation. ¿ American Geophysical Union 1987