A method for feeding a shingled stack of sheet material to a downstream processing device includes the step of identifying a discontinuity in the shingled stack of sheet material wherein the discontinuity has a length dimension from an aft end of a downstream portion of the shingled sheet material to a forward end of an upstream portion of the shingled sheet material. In a next step, the motion of first and second serially arranged conveyors are controlled such that the length dimension of the discontinuity is substantially equal to a prescribed gap of known length dimension. The first conveyor supports the upstream portion of the shingled sheet material and the second conveyor supports the downstream portion of the shingled sheet material. The deck of the first is advanced over the deck of the second conveyor toward the aft end of the downstream portion by the length dimension of the prescribed gap. The upstream portion is then dispensed into shingled engagement with the downstream portion to produce a continuous stack of shingled sheet material.