In a recent paper (G. Worth, P. Hunt and M. Robb, J. Phys. Chem. A, 2003, 107, 621), we used surface hopping direct dynamics calculations to study the molecular dynamics of the butatriene radical cation in the X/A manifold, which is coupled by a conical intersection. Here, we present the first direct dynamics calculations using a novel algorithm, again using this ideal test system. The algorithm, which is based on the powerful multi-configuration time-dependent Hartree (MCTDH) wavepacket propagation method, uses a variational basis of coupled frozen Gaussian functions that optimally represent the evolving nuclear wavepacket at all times. Each Gaussian function follows a "quantum trajectory", along which the potential surface is evaluated by quantum chemistry calculations. As far fewer Gaussian functions are needed than classical trajectories in a semi-classical method, the number of quantum chemical calculations is drastically reduced. A crucial point in direct dynamics. To validate the method, initial calculations have been made using an analytic model Hamiltonian, where it is shown to reproduce the main features of the state population transfer with 8-16 basis functions per state. Coupled to the GAUSSIAN quantum chemistry program, the method is then shown to provide a feasible direct dynamics algorithm for the description of this non-adiabatic process.