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Plants colonized the terrestrial environment over 450 million years ago. Since then, shoot architecture has evolved in response to changing environmental conditions. Our current understanding of the innovations that altered shoot morphology is underpinned by developmental studies in a number of plant groups. However, the least is known about mechanisms that operate in ferns--a key group for understanding the evolution of plant development. Using a novel combination of sector analysis, conditional probability modelling methods and histology, we show that shoots, fronds ('leaves') and pinnae ('leaflets') of the fern Nephrolepis exaltata all develop from single apical initial cells. Shoot initials cleave on three faces to produce a pool of cells from which individual frond apical initials are sequentially specified. Frond initials then cleave in two planes to produce a series of lateral merophyte initials that each contributes a unit of three pinnae to half of the mediolateral frond axis. Notably, this iterative pattern in both shoots and fronds is similar to the developmental process that operates in shoots of other plant groups. Pinnae initials first cleave in two planes to generate lateral marginal initials. The apical and marginal initials then divide in three planes to coordinately generate the determinate pinna. These findings impact both on our understanding of fundamental plant developmental processes and on our perspective of how shoot systems evolved.