No, the previous letter was not an attempt to contradict Romans 4 with James 2.

Romans 4:1 ¶ What shall we say then that Abraham our father, as pertaining to the flesh, hath found?
 2 For if Abraham were justified by works, he hath whereof to glory; but not before God.
 3 For what saith the scripture? Abraham believed God, and it was counted unto him for righteousness.
 4 Now to him that worketh is the reward not reckoned of grace, but of debt.
 5 But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness.

Romans 4 & James 2 do not contradict each other.
Paul is writing about works not being a condition for salvation.
James is writing about the necessity of works as the result of salvation.

Paul, like he also mentioned in Romans 3,

Romans 3:27 Where is boasting then? It is excluded. By what law? of works? Nay: but by the law of faith.
 28 Therefore we conclude that a man is justified by faith without the deeds of the law.

is showing that works is totally absent as a condition, or precondition, for salvation.

Both Paul and James refer to Abraham, and refer to Genesis 15:6.
Paul is talking about what happened when Abraham believed, he was justified by faith.
James is talking about what happened later, as a result of Abraham believing, in fact, many years later:

 James 2:21 Was not Abraham our father justified by works, when he had offered Isaac his son upon the altar?
 22 Seest thou how faith wrought with his works, and by works was faith made perfect?
 23 And the scripture was fulfilled which saith, Abraham believed God, and it was imputed unto him for righteousness: and he was called the Friend of God.
 24 Ye see then how that by works a man is justified, and not by faith only.

In line 23, James referred to Genesis 15:6,  but in line 21, he referred to Genesis 22:1-18, many years later.
What happened in Genesis 22, was a "result" of Abraham believing God in Genesis 15.
Abraham was already justified by faith, when the LORD counted it unto him for righteousness, when he believed God.
That was before the LORD.
Years later, as a result of that very faith, Abraham was offering Isaac on the altar. (he was stopped from doing so)
James said he was thus justified by works, but to whom?
It wasn't to the LORD, as that occurred in chapter 15, by faith.
It was to Abraham himself, to Isaac, and to everyone reading the book of Genesis.

Works do not justify us to the LORD.
Works did not justify Abraham to the LORD, either.
We, like Abraham, need to be justified by faith to the LORD.

However, we are justified before men, by works.
Paul wrote:

Romans 4:2 For if Abraham were justified by works, he hath whereof to glory; but not before God.

The work that Abraham did, in Genesis 22, justified him before men, for 4,00 years, now.
The LORD does not need to see our works in order to know what is in our hearts.
Men cannot see what is in our hearts, men can only see our works.
The works, then, are outward manifestations of an inward transformation.

Our works cannot pay for any sins - no, not in any dispensation.
How many times would someone have to honor their father and mother to pay for only one sin? 10? 100? 1,000?
How many times would someone have to love their neighbor as their-self to pay for only one sin? 10? 100? 1,000?
Keeping commandments does not pay for sins, neither in order to get saved, or to attempt to stay saved.
Eternal life is not the result keeping of the law.
However, good works are a result of having eternal life.

As far as salvation, before the LORD, we are justified by faith, not by the works of the law:

Romans 5:1 Therefore being justified by faith, we have peace with God through our Lord Jesus Christ:

Galatians 2:16 Knowing that a man is not justified by the works of the law, but by the faith of Jesus Christ, even we have believed in Jesus Christ, that we might be justified by the faith of Christ, and not by the works of the law: for by the works of the law shall no flesh be justified.

Galatians 3:11 But that no man is justified by the law in the sight of God, it is evident: for, The just shall live by faith.
 24 Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith.

We are also not justified by the works of the law in order to stay saved, either:

Galatians 5:4 Christ is become of no effect unto you, whosoever of you are justified by the law; ye are fallen from grace.

Yet, the good works are a result of what happened in our hearts by faith, like it did with Abraham.
By our good works we are justified before men, not before God.
Our justification with the LORD occurred the moment we repented and believed on Jesus Christ.

So Romans does not contradict James, and James does not contradict Romans.
Both books are inspired scripture.
The Holy Ghost didn't inspire Paul to contradict the Holy Ghost inspiring James.
That would be ludicrous, false doctrine, and bordering on blasphemy.
The Holy Ghost is not the author of confusion.
The only confusion would be with us, in our minds.

Paul was referring to works as not being a "condition for" salvation.
James was referring to works as a necessary "result of" salvation.

Gino