We develop a notion of higher-order connector towards supporting the systematic construction of architectural connectors for software design. The idea is that individual properties of connectors, such as security and fault-tolerance, can be designed separately as higher-order connectors. Complex connectors can then be described as suitable combinations of higher-order connectors and basic connectors. We use CommUnity, a Unitylike parallel program design language that we have been using for formalising aspects of architectural design, for illustrating our approach to the compositional construction of connectors and also to motivate the categorical semantics of higher-order connectors that we propose.