The question about the relationship between intellectual and creative abilities still remains unresolved. One potential advance in this area of research could be associated with the use of novel methods of divergent thinking assessment. One of the promising tools for assessment of divergent thinking appears to be the old/new scoring method. This study aimed to investigate the role of fluid intelligence in generating “old” (retrieved from memory) and “new” (generated on the spot) ideas distinguished by the old/new scoring method. Two divergent thinking tasks (Guilford's Alternate Uses for a newspaper and a wooden ruler), which were later scored for creativity (via subjective ratings) and the proportion of new ideas, were administered to 115 university students. Participants then completed three tests of fluid intelligence. Results showed that fluid intelligence correlated weakly with both the proportion and creativity of old and new ideas. However, there was a tendency for a closer association of fluid intelligence with the creativity of new ideas but not old ones. We also replicated the serial order effect showing that new ideas rated by both judges and participants as more creative tend to appear later in a response set. However, we did not find any support for the idea that fluid intelligence moderated the serial order effect. Overall, the application of the old/new scoring method did not reveal any complex relationship between fluid intelligence and the proportion and creativity of old and new ideas.