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Multi-output rotation symmetric Boolean functions with good properties play an important role in the design of cryptographic systems. Based on the action of cyclic group on the n-dimensional vector space over binary field, the sufficient conditions for the existence of multi-output k-rotation symmetric balanced and 1-resilient Boolean functions are studied by using the method of orbital partition and constructing orthogonal tables respectively. When n/k = p' (p is prime,r ∈ Z+),the range of values given for m when a balanced or 1-resilient multi-output rotational symmetric Boolean function exists. The concrete construction methods are provided and verified by Matlab. [ABSTRACT FROM AUTHOR]