The reciprocating saw has two, superimposed, blades having a common axis and arcuate cutting surfaces adjacent each other. Part of one blade extends through an opening in the other blade so that the cutting edge of an upper blade is under the cutting edge of a lower blade. The blades' cutting edges extend around the blade or along a smaller arc. A linkage in the saw converts rotary motion of a motor into synchronous, counter-reciprocating motion of the blades about the axis. Counter-reciprocation minimizes action/reaction forces, which occur when a single reciprocating saw blade changes directions.