An improved Rossi-alpha formula is derived to consider a delayed-neutron contribution to a conditional counting probability defined in the Rossi-alpha technique. The improved formula has an additional constant term and another additional term proportional to time interval tau to the original formula. For an university training and research reactor of Kindai University, the Rossi-alpha analyses based on the original and the improved formulae are carried out to examine the applicability of these formulae to the subcritical thermal reactor. The original formula results in an inconsistent prompt-neutron decay constant with that determined from a previous Feynman-alpha analysis considering delayed neutrons. This difficulty of the original formula originates from the neglect of delayed neutrons. Applying the improved formula leads to a consistent prompt-neutron decay constant. The additional constant term of the improved formula should be considered to determine accurately the decay constant, while the additional proportional term is much too small to consider. The additional constant term obtained from the present analysis is consistent with that from the previous Feynman-alpha analysis.