This paper addresses the issue of how negative components affect people's ability to draw conditional inferences. The study was motivated by an attempt to resolve a difficulty for the mental models theory of Johnson-Laird and Byrne, whose account of matching bias in the selection task is apparently inconsistent with Johnson-Laird's explanation of the double negation effects in conditional inference reported by Evans, Clibbens, and Rood (1995). Two experiments are reported, which investigate frequencies of conditional inferences with task presentation similar to that of the selection task in two respects: the presence of a picture of four cards and the use of implicit negations in the premises. The latter variable was shown to be critical and demonstrated a new phenomenon: Conditional inferences of all kinds are substantially suppressed when based on implicitly negative premises. This phenomenon was shown to operate independently of and in addition to the double negation effect. A third experiment showed that the implicit negation effect could be extended to the paradigm in which people are asked to produce their own conclusions. It is argued that these two effects can be explained within either the mental models theory or the inference rule theory, of propositional reasoning, but that each will require some revision in order to offer a convincing account.