Power Transfer Distribution Factors (PTDFs) play a crucial role in power grid security analysis, planning, and redispatch. Fast calculation of the PTDFs is therefore of great importance. In this paper, we present a non-approximative dual method of computing PTDFs. It uses power flows along topological cycles of the network but still relies on simple matrix algebra. At the core, our method changes the size of the matrix that needs to be inverted to calculate the PTDFs from N × N, where N is the number of buses, to (L-N+1) × (L-N+1), where L is the number of lines and L-N+1 is the number of independent cycles (closed loops) in the network while remaining mathematically fully equivalent. For power grids containing a relatively small number of cycles, the method can offer a speedup of numerical calculations.