A novel class of exact-repair regenerating codes is introduced for a distributed storage system with arbitrary parameters (n,k,d). The proposed construction is based on the optimum determinant codes for (n,k=d,d) systems. This construction yields a lower bound for the trade-off between the storage and the repair bandwidth, consisting of k corner points. This bound meets the optimum trade-off for the MBR and MSR points, and improves all the previously known bounds for interior points. The sub-packetization level of the proposed code only depends on k and d, not number of nodes n. Further, the required field size for the proposed code is of order of n. We conjecture that the proposed codes can universally achieve the optimum trade-off for all corner points.