A submersible well pump assembly using threaded connections, the submersible well pump assembly having a first housing, a second housing, a clamp ring, and at least one anti-rotation member. The first housing has an end having an outer surface, an end face, and a shoulder on that outer surface. The second housing has an end having an outer surface and an end face. The outer surface of the second housing has external threads formed thereon and the end face of the second housing abuts the end face of the first housing. The clamp ring is rotatably and slidably carried on the first housing and has internal threads that engage the external threads of the second housing. The clamp ring also has an internal shoulder that engages the shoulder of the first housing. To keep the connection secure, the assembly has at least one anti-rotation member having a cooperative element on each end of each housing to inhibit rotation of one housing relative to the other.