The word "converse" is already a complete word with its own meaning. You can, however, use prefixes to change its meaning, like:
* Counterconverse: This word, though uncommon, means "a statement that opposes a converse" or "the opposite of a converse."
* Nonconverse: This word means "not a converse," often used in logic to refer to a proposition that doesn't follow the rules of a converse.
Important Note: "Converse" is usually used as a verb or a noun, and there's rarely a need to add a suffix to it.