Pattern matching techniques such as matched filtering will be used for online extraction of gravitational wave signals buried inside detector noise. This involves cross correlating the detector output with hundreds of thousands of templates spanning a multi-dimensional parameter space, which is very expensive computationally. A faster implementation algorithm was devised by Mohanty and Dhurandhar using a hierarchy of templates over the mass parameters, which speeded up the procedure by about 25–30 times. We show that a further reduction in computational cost is possible if we extend the hierarchy paradigm to an extra parameter, namely, the time of arrival of the signal. In the first stage, the chirp waveform is cut-off at a relatively low frequency allowing the data to be coarsely sampled leading to cost saving in performing the FFTs. This is possible because most of the signal power is at low frequencies, and therefore the advantage due to hierarchy over masses is not compromised. Results are obtained for spinless templates up to the second post-Newtonian (2PN) order for a single detector with LIGO I noise power spectral density. We estimate that the gain in computational cost over a flat search is about 100, which is about a factor of four over the previous less sophisticated hierarchical scheme.