Abstract : We present a new globally optimal algorithm for self- calibrating a moving camera with constant parameters. Our method aims at estimating the Dual Absolute Quadric (DAQ) under the rank-3 and, optionally, camera centers chirality constraints. We employ the Branch-and-Prune paradigm and explore the space of only 5 parameters. Pruning in our method relies on solving Linear Matrix Inequality (LMI) feasibility and Generalized Eigenvalue (GEV) problems that solely depend upon the entries of the DAQ. These LMI and GEV problems are used to rule out branches in the search tree in which a quadric not satisfy- ing the rank and chirality conditions on camera centers is guaranteed not to exist. The chirality LMI conditions are obtained by relying on the mild assumption that the camera undergoes a rotation of no more than 90◦ between consec- utive views. Furthermore, our method does not rely on cal- culating bounds on any particular cost function and hence can virtually optimize any objective while achieving global optimality in a very competitive running-time.