Notice Period

I wish to seek your expertise on this matter. I have been working for this company initially as a Part-time Administrator and my contract was signed by the previous management on 21 July 2010. But on the 01 January 2011, the new management offered me a Permanent position as an Executive Assistant. The new contract was not signed by both parties. I have intended to resigned from the company last year on 24 February 2011 but after they a few round of talk, I decided to stay but my salary was lowered by $400.

All these were verbal and no new contract was provided. Now after another year with the company, I totally give up with their management profesionalism. They have deferred my AWS till further notice. Recently, the company went thru a change of company's name but no change of directorship. I wish to tender my resignation giving them 24 hour notice, since there are not contract signed. The Employer requested me to give them 1 month instead else pay them the notice period. My question is, am I binded with any legal contract with the employer? Do I need to give them any notice period at all?

Based on Employment Act, in the absence of the Letter of Appointment or contract, the notice peiod as follows:
  • Length of service less than 26 weeks, 1 day notice
  • Length of service 26 weeks to less than 2 years, 1 week notice
  • Length of service 2 years to less than 5 years, 2 weeks notice
  • Length of service 5 years and above, 4 weeks notice