This is another question I get often about HotMail. All I can figure is that HotMail's own documentation on your Secret Question must be lacking somehow.
Whatever the case, let me walk you through it:
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First, you must be able to log in. If you cannot login to HotMail, you cannot change your secret question. Period. See the links to related articles for some help if you cannot login.
Once you've logged in to MSN HotMail, in the upper right hand corner is a link labeled Options:

Click that.
On the resulting page, you'll find a link labeled Secret Question:

Clicking that will take you to the "Change your question and secret answer" page:

You'll need to enter your password, select one of the secret questions that HotMail provides, and enter your secret answer, and press continue. That's all there is to it:

IMPORTANT: do not forget your secret question and answer. If you do forget it, AND you forget your password, you may loose your account, and all email and contacts within it.
Article C2389 - July 21, 2005
Changed password OK after today's scare in the press - except now I can't get access. Tried the reset route leading to the secret question, which is annotated 'my wife'. But - what is the question? I don't know what to put in the box. Do you have the list of questions to help decide? Please send response alternative email above, as Hotmail account is now not accessible.
Posted by: Pierre Miles at October 6, 2009 3:47 PMReference my question dated 6 October 2009: I managed to contact the MS Customer Service people who were extremely helpful. They asked me a number of questions so that they could ensure that I was the rightful owner of the account and then provided a temporary link to the account to enable me to re-establish control of it. It all worked perfectly. New password and new secret question - all working.
Posted by: Pierre Miles at October 23, 2009 6:07 AMSo, full marks to Microsoft for excellent service.
I need to change the answer to my secret password and then reset again. I remember my old password.
Posted by: karen Ramdin at January 7, 2010 10:27 AMhow can i change my secret question? i know the password but i has been closed so what can i do??
Posted by: kireet at February 4, 2010 8:19 AMMy friend has another secret question, and that is; What do you fill the box with?
Posted by: Diego at March 12, 2010 2:05 PMI don't know how to INVENT my secret answer, like he did. Can youshow me how?