1 Introduction

Many gamma-ray bursts which were too weak to cause the BATSE to trigger or were being missed due to other reasons (data readouts etc.) can be confidently identified in the BATSE daily records which cover the full period of the CGRO operation.

The systematic search for non-triggered GRBs was started by Kommers et al. (1997). Recently, Kommers et al. (1998) completed the data scan for 6 years.

Despite that we started our search (in November, 1997) for non-triggered bursts much later than Kommers et al. (1997), the motivation of the work was that we started our scan with some important advances. Firstly, we used a more selective off-line trigger code. Secondly, and most importantly, is the method of measurement of the efficiency of the GRB search using artificial test bursts that we employed.