IT is now doubly urgent that the government of President Frederik de Klerk prove it is serious about ending the violence between rival black political groups in South Africa. That would be one way of showing it's capable of the good faith needed to negotiate a better future for the country.Such good faith is seriously in doubt following disclosures of government funding for the Inkatha Freedom Party, headed by Zulu Chief Mangosuthu Buthelezi. With official funds going to Inkatha, how can the government be even-handed in dealing with the strife between the Zulu movement and the African National Congress? How can Mr. De Klerk be a neutral party wanting only to help shape a new, more just South Africa? The ANC has long charged government duplicity in the violence between its supporters and those of Inkatha. De Klerk has denied a pro-Inkatha policy exists, but has been slow to disarm the Zulus and shut down the worker hostels widely viewed as seedbeds of violence. The government has started an investigation of charges that its defense forces were involved in the massacre of civilians aboard a Soweto train last September. But as indications of official complicity in black-on-black fighting mount, De Klerk may have to go beyond such probes. He may have to fire some top police and defense officials. Calls are being heard, after all, for De Klerk's own removal. The president has to establish that he is in charge and won't countenance assaults on public order by those who should be preserving it. Now that Law and Order Minister Adriaan Vlok and Foreign Minister Roelof F. Botha have confirmed the government's financial links to Inkatha, other charges - like government arming of Zulus with AK-47 rifles - are likely to gain new currency. Official backing for the Inkatha party and its affiliated labor union was intended to nurture an alternative black political force, opposed to the ANC and aligned with Pretoria. The past week's disclosures, however, discredit Chief Buthelezi. They support allegations that he's the government's man. De Klerk has no choice now but to mend bridges to the ANC, headed by Nelson Mandela. Mr. Mandela, however, has said that the Inkatha funding puts the government on a "collision course" with the ANC. But De Klerk can avoid that collision. By taking strong action to clean up the police/Inkatha mess, he can show himself a "man of integrity," as Mandela once described him. Then the country can get on with the negotiations so critical to its future.