Shihonage

Shihonage is the "four-directions" throw, or the "all-directions throw." It is derived from a practice in kendo of practicing menuchi to the front, left, right, and back. With the two hands on the sword, the basic form of shihonage looks a lot like the four-directions cutting exercise. The implication of the name of the technique is that you can throw uke any direction with it or that you can throw uke with this technique whatever direction he happens to be travelling in.
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I currently favor the last interpretation - that however uke happens to be stepping there is an opportunity for shihonage to occur. This interpretation of shihonage jives well with the 2 variants we practice in hanasu and the variants we practice in nijusan. There are three primary variants of shihonage that we practice a lot, including the traditional shihonage, tenkai kotegaeshi, and reverse kotegaeshi.
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There is an interesting article on the web about one sensei's opinion that the term "nage" as part of the name of a throw is counterproductive because it puts tori into a mindset that favors forceful, sudden, ballistic motion (like how you "throw" a baseball or anything else in the world). See also this interesting info and this too about ideokinesis - the concept that changing how you visualize motion changes how you execute motion. This sensei favors the terminology "release," which I very much like because we tend to "release" uke rather than "throwing" uke.
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Thus the central role of the hanasu (release) exercises and the chains built off the hanasu motions. So, it would be cool with me if people called this technique "shiho hanasu" instead of "shihonage," although I don't know if that is proper usage of the Japanese terminology.
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Check out this article for a handful of hints that might help you with your shihonage...

(Photo courtesy of Phineas X)