In order to guarantee pairwise independence of codewords in an ensemble of convolutional codes it is necessary to consider time-varying codes. However, Seguin has shown that the pairwise independence property is not strictly necessary when applying the random coding argument and on this basis he derives a new random coding bound for rate 1/n fixed convolutional codes. In this paper we show that a similar random coding bound can be obtained for rate k/n fixed convolutional codes.