Josephson junctions with a phase drop of pi in the ground state allow us to create vortices of supercurrent carrying only half of the magnetic flux quantum Phi0 approximately 2.07 x 10(-15) Wb. Such semifluxons have twofold degenerate ground states denoted upward arrow (with flux +Phi0/2 and supercurrent circulating clockwise) and downward arrow (with flux -Phi0/2 and supercurrent circulating counterclockwise). We investigate a molecule consisting of two coupled semifluxons in a 0-pi-0 long Josephson junction. The fluxes (polarities) of semifluxons are measured by two on-chip SQUIDs. By varying the dc bias current applied to the 0-pi-0 junction, we demonstrate controllable manipulation and switching between two states, upward arrow downward arrow and downward arrow upward arrow, of a semifluxon molecule. These results provide a major step towards employing semifluxons as bits or qubits for classical and quantum digital electronics.