A suffix vector of a string is an index data structure equivalent to a suffix tree. It was first introduced by Monostori et al. in 2001 [9, 10, 11]. They proposed a linear construction algorithm of an extended suffix vector then another linear algorithm to transform an extended suffix vector into a more space economical compact suffix vector. We propose an on-line linear algorithm for directly constructing a compact suffix vector. Not only we show that it is possible to directly build a compact suffix vector but we will also show that this on-line construction can be faster than the construction of the extended suffix vector. Finally, we present an efficient method for computing maximal repeats using suffix vectors.