An interesting topic has been the possible behavior of transient fields in the limit of great distances from their sources. Under the physical restriction that the total energy radiated is finite, it has been shown that the energy reaching a distant receiver can decrease with distance much more slowly than the usual r−2. Such cases of slow decrease have been referred to as electromagnetic missiles. All of the wide variety of known missiles propagate in essentially straight lines. It is shown here that such a missile can follow a path that is strongly curved. An example of a curved electromagnetic missile is explicitly constructed and some of its simpler properties are discussed.