Schools watchdog Ofsted has said it will make changes after the suicide of head teacher Ruth Perry in January.
Chief inspector Amanda Spielman said Ofsted was piloting changes to its complaints system, but added the single overall grade for schools would stay.
Ms Perry took her own life while waiting for Ofsted to publish a report grading her school Inadequate.
Her sister Julia Waters told BBC News she wanted inspections to be paused, to allow a full review.
Ofsted has said its thoughts are with Ms Perry’s family, and described her death as a tragedy.
Prof Waters told BBC News condolences weren’t enough, and said the family had not heard directly from Ofsted about the concerns the family has raised.
“It adds to the hurt, it adds to the outrage, it adds to our feeling of injustice about what happened to Ruth,” she said.
The family believes the anxiety and stress following the inspection led to Ms Perry’s suicide.
Prof Waters said she had been overwhelmed by the number of people getting in touch and speaking out about Ofsted.
“It is a potentially dangerous system,” she told BBC News, adding that a pause in inspections would be the “decent, empathetic, human thing to do”.
She wants an independent inquiry into what happened at Ms Perry’s school and a review of the culture of inspections at Ofsted.
In her statement, Ms Spielman said Ofsted “won’t be soft on safeguarding”, but where a school is otherwise doing well they will try to visit again more quickly to reflect improvements in their judgements.
Ofsted is also holding briefings for head teachers whose schools have not been inspected for a long time, she said.
“We are not deaf to the calls for change, or insensitive to the needs of schools and their staff,” she added. “We will continue to listen carefully to the experiences and views of those we inspect.”
Caversham Primary School was downgraded by Ofsted after inspectors decided that checks on staff and record keeping of concerns about children were inadequate.
Under the current system, this means the leadership of the school is declared inadequate, as well as the school overall.
The quality of education and behaviour at the school were praised by inspectors.
Before the Covid-19 pandemic, most schools were inspected roughly once every four years. However all visits were put on hold in the pandemic.
Outstanding schools were also exempt for eight years up to 2020, which means some are now now facing inspection for the first time in a decade.
Some academy school leaders have said Ofsted is not fully considering the impact of the pandemic.
Education Secretary Gillian Keegan said standards on keeping children safe would not be “watered down”, and she continued to support a “clear one-word rating” to inform parents’ decisions.
She told MPs earlier this week she would be willing to meet Ms Perry’s family.
Head teachers’ unions said the changes did not go far enough, and failed to recognised the strength of feeling among teachers.
Geoff Barton, general secretary of the Association of School and College Leaders (ASCL), said: “The reality is that Ofsted has completely lost the trust of leaders and teachers, and it will take a great deal more than this to gain their confidence.”
In March, the National Education Union (NEU), school leaders’ union NAHT, and the ASCL called for inspections to be halted.
The recruitment process for a new chief inspector of Ofsted is already under way, because Ms Spielman is standing down later this year.
Prof Waters says change can’t wait until then.
“There is an urgent problem in Ofsted, and it needs to be dealt with urgently,” she said.
“What happened to Ruth could happen again.”
A full inquest will consider the circumstances around Ruth Perry’s suicide later this year.