I found the following link on the web which explains quite well the steps I need to follow to calculate Axes points of probability contours.

In slide 21 they have calculated eigenvalue and eigenvector but it is not what I get from Octave or C# libraries.

In both cases I get the following vector [-0.965,0.260;0.260,0.965], the values are OK but according to the presentation I should have got [0.965, -0.260; 0.260, 0.965]. The minus sign is in the different position and skewes final results.

Could anyone tell me what additional step I need to take in order to get to the results they have in the presentation?

Slide 24 is basically what I need to do.