Although Spectre's response is absolutely correct in the traditional sense, there is one very good company that produces machinery which creates a coil that imparts no twist when the wire is unwound, inertia free and without rotation, from the inside of the coil.
The machine is high speed and not cheap. It is used to make pay off coils for data cable, telephone cable for houses, and building wire. You can see a few of the various sized cardboard packages that hold these coils at any big box hardware center or at any electrical distributor.
When the coil is manufactured, a radial opening for a polymeric wire guide (Also supplied by the company.) to bring the wire from the inside the coil is "woven" into the coil by microprocessor control.
The analogy as to the way it works is to think of creating a figure 8 on the ground with wire and then picking it up at the spot where the wires cross each other. (At the center of the figure 8 so to speak.) This would give you two coils of continuous wire, side by side with one twisted left and one twisted right. Thus there is no algebraic twist when the wire is pulled out from the inside of of the coil because the opposite direction of each coil cancels the twists out.
In real life, the coil is spooled on a mandrel and the key to the process is a very high speed traverse so that the left/ right coil effect is achieved. We are sure you can now visualize this in your mind knowing the analogy above. The cross over position is also adjusted around the circumference of the coil by microprocessor control both to maintain the coil dimensions and to "weave" the hole for the wire guide.
The company you say? Windings Inc. at
www.reelex.com/
I think this is all the information you require.
Kindest regards,
Peter J. Stewart-Hay
Principal
Stewart-Hay Associates
www.Stewart-Hay.com 
