A reaction between two scalars in a turbulent channel flow has been investigated by means of a direct numerical simulation. One side of the channel has a solid no-slip wall, the other side a free-slip surface. One of the scalars is released from a small continuous line source situated in the shear layer near the solid wall. The reaction and its magnitude occur very intermittent the flow. Modelling of the reaction rate term is therefore difficult, one of the methods applied in this case is the conditional moment closure technique. Some features of the conditional moments have been investigated here. It is shown that conditioning of the mean concentration on the mixture fraction reduces the cross-stream variation of the mean concentration significantly. Furthermore it is found that the reaction term in the conditional moment closure approach can be relatively easily modelled. Therefore, conditional moment closure seems to be a promising approach for the modelling of reactions in turbulent shear flows.