The analysis in this paper was based on five Malay narratives of the "frog story". In these narratives, the types of lexical arguments and their relations with information flow and topic continuity were analyzed. It was found that most narrators used one lexical argument in telling the frog story (e.g., sarang itu jatuh "the nest fell"). About 60% of the verbs in the narratives contained one lexical argument only. Some transitive verbs that usually require the presence of both lexical arguments were used with one lexical argument only when produced in speech (e.g., dia mencari ø di merata tempat "he searched (for) ø everywhere"). Objects were sometimes omitted, as their meanings could be predicted from previous context. Despite the omission of objects, transitive constructions still prevailed in the stories. The most frequently occurring lexical arguments were objects (o) (37%), followed by intransitive subjects (s) (29%) and transitive subjects (a) (27%). In addition, our results showed that new information in Malay was usually allocated to the core argument of the object and to locative expressions, indicating that most of the new information appeared at the end of a clause. On the other hand, topic continuity was held between the subjects in two continuous intonation units. This clear-cut division of discourse functions in the heads and tails of constructions was consistently found in the five pieces of narration. This observation not only showed how ideas could be continued in Malay oral narratives, but also contributes to the study of discourse structure in Malay.