We present a first-principles method for the evaluation of the transmittance probability and the coherent conductance through elongated systems composed of a repeating molecular unit and terminated at both ends. Our method is based on a divide and conquer approach in which the Hamiltonian of the elongated system can be represented by a block tridiagonal matrix, and therefore can be readily inverted. This allows us to evaluate the transmittance and the conductance using first-principles electronic structure methods without explicitly dealing with calculations involving the entire system. A proof of concept model based on a trans-polyacetylene chain bridging two aluminum leads indicates that our divide and conquer approach is able to capture all of the features appearing in the transmittance probability curves of a full scale calculation.