The Australian sharemarket has recorded its best session in seven weeks on Tuesday, extending its rally and exiting its 11-week bear market.

The S&P/ASX 200 Index rose 164.4 points, or 2.9 per cent, to 5780, extending its strong rise in Monday's session and recording consecutive gains above 2 per cent for the first time in two months.

CSL rose 3.1 per cent to $307.63 however it was the banks that truly shone.

Commonwealth Bank rose 3.9 per cent to $61.31, Westpac advanced 6.3 per cent $16.30, NAB climbed 5.7 per cent to $16.64 and ANZ firmed 6 per cent to $16.52.

Southern Cross Media Group firmed 15.6 per cent to 19¢, Unibail-Rodamco-Westfield rose 12.7 per cent to $3.99 and SmartGroup climbed 12.7 per cent to $6.59.

Afterpay closed at a record high of $49.11, up 1.3 per cent for the session after clearing $50 earlier in the day.

Fortescue Metals Group was one of the 20 stocks inside the top 200 that traded lower, falling 0.4 per cent to $13.78.

Pinnacle Investments fell 2.6 per cent to $4.05, GrainCorp slid 2.4 per cent to $4.10 and Mayne Pharma declined 2.2 per cent to 44¢.