Reachability analysis is one major approach for safety verification of continuous and hybrid dynamical systems. In this paper we present a new approach to calculate the reachable states of linear systems with uncertain inputs under the assumption that the inputs are stepwise constant. The original systemSwith inputs is transformed into a systemS0without inputs such that the reachability problem ofScan be reformulated as a problem that involves onlyS0and thus the inputs need no longer to be considered. Finally, we show that this approach is in accordance with existing ones.