Even if Australian Prime Minister Tony Abbott "snubbed" the invitation of Indonesian President Susilo Bambang Yudhoyono to an international conference in Bali a few weeks ago, the icy diplomatic relations between Canberra and Jakarta have started thawing.

The sign is the return of Indonesian Ambassador to Australia Najib Riphat Kesoema to Canberra. The envoy was recalled by the president in November at the height of the spying allegations against Australia.

Australian Foreign Minister Julie Bishop used the announcement of the ambassador to his assignment to blame the Labor government which tapped the mobile phone of Mr Yudhoyono, his wife and several ministers.

The incident led Indonesia to suspend normal co-operation with Australia on the latter's asylum boat policy, while Indonesia demanded an apology and sought the signing of a code of conduct before they resume joint efforts on common problems such as people smuggling, defence and intelligence sharing.

Bishop had already sent the draft of the code of conduct to Indonesian Foreign Minister Marty Natalegawa in December, but it hasn't been signed yet. Mr Yudhoyono hopes the agreement would be inked by August, which would be the final confirmation of resumption of normal diplomatic ties between the two neighours.