The matter is not without controversy, even among Muslims:

Muslim groups in the United States disagree as to how the qibla should be oriented - some believe that the direction should be calculated as a straight line drawn on a flat map, like the familiar Mercator projection of the globe; others say that the direction is determined by the shortest line on the globe of the earth, or a great circle. At times this controversy has lead to heated disputes. Flat-map Muslims in the United States pray east and slightly south; great-circle Muslims face in a north-easterly direction.

--from Wikipedia (see link above)