A method for recovering from three failed data storage devices is disclosed. A plurality of data storage devices hold data, and a row parity storage device holds row parity for them. The data storage devices and the row parity storage device form a set of storage devices. A diagonal parity storage device and an anti-diagonal parity storage device hold parity computed diagonally over the set of storage devices. In the event of a failure of three data storage devices of the set of storage devices, a first failed storage device is chosen for first restoration. A missing block of the first failed storage device is computed by using the remaining set of storage devices, and the diagonal parity storage device, and the anti-diagonal parity storage device. The remaining two failed storage devices are restored by a diagonal parity restoration technique.