A rights issue is an allotment of shares to existing shareholders in accordance with their current shareholdings of that class of shares. Payment for the shares is made by the shareholder and usually this is in full in cash on acceptance of the shares.
This is not to be confused with a 'bonus issue' which, although similar is different in that issues are in accordance with shareholders dividend rights and the shares are paid for in full from the undistributed reserves of the Company.
A 'Rights Issue' may be non-renounceable - which means that only the allottee may accept the offered shares or renounceable - which means that shares can be accepted in favour of third parties.
NOTE: Care must be taken not to infringe the restrictions relating to public offer of shares (by a private company) and it is recommended that professional advice is sought as a breach of these conditions could render the company and its officers guilty of a serious offence.