Due to the variations in the local solidification conditions in typical industrial casting processes, dendrites grow under transient rather than steady-state conditions. In this study, the phase-field method was used to study the evolution of secondary dendrite arms of Fe-0.3 wt.% C alloy during transient directional solidification imposed by decreasing the pulling velocity. We find that the dendrite under transient growth conditions is different from the steady-state dendrite, with smaller selection parameter e and the dendrite envelope inside the parabola scaled by the tip radius. The secondary arms undergo a ripening process in which other secondary arms remelt by shrinking from their tips, rather than by detachment from the primary stalk. The surviving arms are finer than those found under steady-state growth conditions, and the size of the surviving arms decreases with decreasing growth velocity.