Cumulative cultural evolution occurs when social traditions accumulate improvements over time. In humans cumulative cultural evolution is thought to depend on a unique suite of cognitive abilities, including teaching, language and imitation. Tool-making New Caledonian crows show some hallmarks of cumulative culture; but this claim is contentious, in part because these birds do not appear to imitate. One alternative hypothesis is that crows' tool designs could be culturally transmitted through a process of mental template matching. That is, individuals could use or observe conspecifics' tools, form a mental template of a particular tool design, and then reproduce this in their own manufacture - a process analogous to birdsong learning. Here, we provide the first evidence supporting this hypothesis, by demonstrating that New Caledonian crows have the cognitive capacity for mental template matching. Using a novel manufacture paradigm, crows were first trained to drop paper into a vending machine to retrieve rewards. They later learnt that only items of a particular size (large or small templates) were rewarded. At test, despite being rewarded at random, and with no physical templates present, crows manufactured items that were more similar in size to previously rewarded, than unrewarded, templates. Our results provide the first evidence that this cognitive ability may underpin the transmission of New Caledonian crows' natural tool designs.