In this paper, we present efficient algorithms for finding indeterminate Arc-Annotated patterns in indeterminate Arc-Annotated references. Our algorithms run in O(m + nm w ) time where n and m are respectively the length of our reference and pattern strings and w is the target machine word size. Here we have assumed the alphabet size to be constant, because, indeterminate Arc-Annotated sequences are used to model biological sequences. Clearly, for short patterns, our algorithms run in linear time and efficient algorithms for matching short patterns to reference genomes have huge applications in practical settings. We have also applied our algorithms to scan the ncRNAs without pseudoknots. We scanned three whole human chromosomes and it took only 2.5 - 4 minutes to scan one whole chromosome for an ncRNA family. Some relevant patents are discussed in [1, 2].