Simply changing outward behavior is not repentance. We at times change our behavior for self-centered reasons. Sometimes we change in an attempt to atone for my sins.  Such change will only make my sinfulness more sinful.

This is the basis for the reference in Hebrews of repenting from ‘dead works'.  A dead work is a work that is not done with the leading and empowerment of the indwelling Holy Spirit.  Hence any good work a non-Christian would attempt is a dead work.  And many types of good works that Christians do could be devoid of the Spirit's leading and empowerment.

• A dead work is giving to charity because it is a good tax break.
• It is going to church because it is good for my business reputation or my resume or my politics.
• It is tithing because I am afraid God will ‘get me' if I don't.
• It is sending my kids to a Christian school, not because I want them to learn the truths of the Christian faith and surrender their lives to the Lordship of Christ, but because there they will run in the right crowd.
• It is the giving up of a sinful habit, not because I want to be controlled by the Spirit of God instead of the habit, but because the habit inhibits my performance at work and is harming my professional reputation.

In all these ways, I have actually changed, but the change has not accomplished what Jeremiah said was impossible:

Can the Ethiopian change his skin
or the leopard his spots?
Then also you can do good
who are accustomed to do evil.