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Magnetic separators, which lie on the boundary between four topologically distinct flux domains, are prime locations in three‐dimensional magnetic fields for reconnection, especially in the magnetosphere between the planetary and interplanetary magnetic fields and also in the solar atmosphere. Little is known about the details of separator reconnection, and so the aim of this paper, which is the first of two, is to study the properties of magnetic reconnection at a single separator. Three‐dimensional, resistive magnetohydrodynamic numerical experiments are run to study separator reconnection starting from a magnetohydrostatic equilibrium which contains a twisted current layer along a single separator linking a pair of opposite‐polarity null points. The resulting reconnection occurs in two phases. The first is short involving rapid reconnection in which the current at the separator is reduced by a factor of around 2.3. Most (75%) of the magnetic energy is converted during this phase, via Ohmic dissipation, directly into internal energy, with just 0.1% going into kinetic energy. During this phase the reconnection occurs along most of the separator away from its ends (the nulls) but in an asymmetric manner which changes both spatially and temporally over time. The second phase is much longer and involves slow impulsive bursty reconnection. Again, Ohmic heating dominates over viscous damping. Here the reconnection occurs in small localized bursts at random anywhere along the separator.