In centered difference models of ocean circulation, two grid-point computational modes can be excited if grid Reynolds and Peclet numbers are greater than two. The Bryan-Cox General Circulation Model (GCM) is used to show the dramatic effect that this instability has on the equatorial thermohaline circulation. In many recent numerical calculations researchers have used 12 vertical levels. It is shown that this resolution produces an artificial cell at the equator when typical values of the vertical diffusivity and viscosity parameters are used. This artifical cell rotates counter to the primary cell driven by deep water formation at high latitudes, is driven by downwelling at the eastern boundary near the equator and is 40% the strength of the primary cell for the parameters used in the present study. When the vertical resolution is increased the cell vanishes. It is suggested therefore that higher vertical resolution should be used in Bryan-Cox GCM deep-ocean modeling studies when current values of the vertical diffusivity and viscosity parameters are used.