In conventional strapdown inertial navigation systems, the coordinate transformation matrix differential equation is integrated in the computer of the system. This computation typically requires 30 to 60 percent of the time budget of the computer. A method is presented in this report for significantly reducing the digital computation burden through the use of hybrid computational techniques. Analog correction signals for the non-commutativity phenomenon are fed onto the gyro torque generators causing the gyros to integrate a vector differential equation in the rotation vector argument of the coordinate transformation matrix. The coordinate transformation matrix is then merely evaluated as a matrix function of the rotation vector argument. A 20 to 1 reduction in the digital computer time budget can thus be realized.